homework 5 statistics

Chapter 5: Continuous Random Variables

Chapter 5 Homework

5.1 homework.

For each probability and percentile problem, draw the picture.

Consider the following experiment. You are one of 100 people enlisted to take part in a study to determine the percent of nurses in America with an R.N. (registered nurse) degree.  You ask nurses if they have an R.N. degree.  The nurses answer “yes” or “no.”  You then calculate the percentage of nurses with an R.N. degree.  You give that percentage to your supervisor.

• What part of the experiment will yield discrete data?
• What part of the experiment will yield continuous data?

When age is rounded to the nearest year, do the data stay continuous, or do they become discrete?  Why?

Age is a measurement, regardless of the accuracy used.

5.2 Homework

Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks).

• X ~ _________
• Graph the probability distribution.
• f ( x ) = _________
• μ = _________
• σ = _________
• Find the probability that a person is born at the exact moment week 19 starts. That is, find P ( x = 19) = _________
• P (2 < x < 31) = _________
• Find the probability that a person is born after week 40.
• P (12 < x | x < 28) = _________
• Find the 70 th percentile.
• Find the minimum for the upper quarter.

A random number generator picks a number from one to nine in a uniform manner.

• P (3.5 < x < 7.25) = _________
• P ( x > 5.67)
• P ( x > 5| x > 3) = _________
• Find the 90 th percentile.
• X ~ U (1, 9)
• Check student’s solution.
• [latex]f\left(x\right)=\frac{1}{8}[/latex] where [latex]1\le x\le 9[/latex]
• [latex]\frac{15}{32}[/latex]
• [latex]\frac{333}{800}[/latex]
• [latex]\frac{2}{3}[/latex]

According to a study by Dr. John McDougall of his live-in weight loss program at St. Helena Hospital, the people who follow his program lose between six and 15 pounds a month until they approach trim body weight. Let’s suppose that the weight loss is uniformly distributed. We are interested in the weight loss of a randomly selected individual following the program for one month.

• Define the random variable. X = _________
• Find the probability that the individual lost more than ten pounds in a month.
• Suppose it is known that the individual lost more than ten pounds in a month. Find the probability that he lost less than 12 pounds in the month.
• P (7 < x < 13| x > 9) = __________. State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.

A subway train on the Red Line arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.

• Define the random variable. X = _______
• X ~ _______
• f ( x ) = _______
• μ = _______
• σ = _______
• Find the probability that the commuter waits less than one minute.
• Find the probability that the commuter waits between three and four minutes.
• Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probability.
• X represents the length of time a commuter must wait for a train to arrive on the Red Line.
• X ~ U (0, 8)
• [latex]f\left(x\right)=\frac{1}{8}[/latex] where ≤ x ≤ 8
• [latex]\frac{1}{8}[/latex]

The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. We randomly select one first grader from the class.

• Find the probability that she is over 6.5 years old.
• Find the probability that she is between four and six years old.
• Find the 70 th percentile for the age of first graders on September 1 at Garden Elementary School.

Use the following information to answer the next three exercises. The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

What is the average waiting time (in minutes)?

Find the 30 th percentile for the waiting times (in minutes).

The probability of waiting more than seven minutes given a person has waited more than four minutes is?

The time (in minutes) until the next bus departs a major bus depot follows a distribution with f ( x ) = [latex]\frac{1}{20}[/latex] where x goes from 25 to 45 minutes.

• Define the random variable. X = ________
• X ~ ________
• The distribution is ______________ (name of distribution). It is _____________ (discrete or continuous).
• μ = ________
• σ = ________
• Find the probability that the time is at most 30 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• Find the probability that the time is between 30 and 40 minutes. Sketch and label a graph of the distribution. Shade the area of interest. Write the answer in a probability statement.
• P (25 < x < 55) = _________. State this in a probability statement, similarly to parts g and h, draw the picture, and find the probability.
• Find the 90 th percentile. This means that 90% of the time, the time is less than _____ minutes.
• Find the 75 th percentile. In a complete sentence, state what this means. (See part j.)
• Find the probability that the time is more than 40 minutes given (or knowing that) it is at least 30 minutes.

Suppose that the value of a stock varies each day from 💲16 to 💲25 with a uniform distribution.

• Find the probability that the value of the stock is more than 💲19.
• Find the probability that the value of the stock is between 💲19 and 💲22.
• Find the upper quartile – 25% of all days the stock is above what value? Draw the graph.
• Given that the stock is greater than 💲18, find the probability that the stock is more than 💲21.

P ( X > 19) = (25 – 19) [latex]\left(\frac{1}{9}\right)[/latex] = [latex]\frac{6}{9}[/latex] = [latex]\frac{2}{3}[/latex].

• The area must be 0.25, and 0.25 = (width)[latex]\left(\frac{1}{9}\right)[/latex], so width = (0.25)(9) = 2.25. Thus, the value is 25 – 2.25 = 22.75.

So, P ( x > 21| x > 18) = (25 – 21)[latex]\left(\frac{1}{7}\right)[/latex] = 4/7.

= [latex]\frac{P\left(x>21\right)}{P\left(x>18\right)}[/latex] = [latex]\frac{\left(25-21\right)}{\left(25-18\right)}[/latex] = [latex]\frac{4}{7}[/latex].

A fireworks show is designed so that the time between fireworks is between one and five seconds, and follows a uniform distribution.

• Find the average time between fireworks.
• Find the probability that the time between fireworks is greater than four seconds.

The number of miles driven by a truck driver falls between 300 and 700, and follows a uniform distribution.

• Find the probability that the truck driver goes more than 650 miles in a day.
• Find the probability that the truck driver goes between 400 and 650 miles in a day.
• At least how many miles does the truck driver travel on the farthest 10% of days?
• P ( X > 650) = [latex]\frac{700-650}{700-300}=\frac{500}{400}=\frac{1}{8}[/latex] = 0.125.
• P (400 < X < 650) = [latex]\frac{700-650}{700-300}=\frac{250}{400}[/latex] = 0.625
• 0.10 = [latex]\frac{\text{width}}{\text{700}-\text{300}}[/latex], so width = 400(0.10) = 40. Since 700 – 40 = 660, the drivers travel at least 660 miles on the farthest 10% of days.

5.3 Homework

Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to eight minutes.

• Define the random variable. X = ________________.
• Is X continuous or discrete?
• Draw a graph of the probability distribution. Label the axes.
• Find the probability that a phone call lasts less than nine minutes.
• Find the probability that a phone call lasts more than nine minutes.
• Find the probability that a phone call lasts between seven and nine minutes.
• If 25 phone calls are made one after another, on average, what would you expect the total to be? Why?

Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery.

• Define the random variable. X = _________________________________.
• On average, how long would you expect one car battery to last?
• On average, how long would you expect nine car batteries to last, if they are used one after another?
• Find the probability that a car battery lasts more than 36 months.
• Seventy percent of the batteries last at least how long?
• X = the useful life of a particular car battery, measured in months.
• X is continuous.
• X ~ Exp (0.025)

The percent of persons (ages five and older) in each state who speak a language at home other than English is approximately exponentially distributed with a mean of 9.848. Suppose we randomly pick a state.

• Find the probability that the percent is less than 12.
• Find the probability that the percent is between eight and 14.
• Why is this number different from 9.848%?
• What would make this number higher than 9.848%?

The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about five years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.

• X ~ = ________
• Find the probability that the person retired after age 70.
• Do more people retire before age 65 or after age 65?
• In a room of 1,000 people over age 80, how many do you expect will NOT have retired yet?
• X = the time (in years) after reaching age 60 that it takes an individual to retire
• X ~ Exp [latex]\left(\frac{1}{5}\right)[/latex]

The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of 💲150.

• Find the probability that a car required over 💲300 for maintenance during its first year.

Use the following information to answer the next three exercises. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

The decay rate is:

What is the probability that a phone will fail within two years of the date of purchase?

What is the median lifetime of these phones (in years)?

Let X ~ Exp (0.1).

• decay rate = ________
• Graph the probability distribution function.
• On the graph, shade the area corresponding to P ( x < 6) and find the probability.
• Sketch a new graph, shade the area corresponding to P (3 < x < 6) and find the probability.
• Sketch a new graph, shade the area corresponding to P ( x < 7) and find the probability.
• Sketch a new graph, shade the area corresponding to the 40 th percentile and find the value.
• Find the average value of x .

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years.

• Find the probability that a light bulb lasts less than one year.
• Find the probability that a light bulb lasts between six and ten years.
• Seventy percent of all light bulbs last at least how long?
• A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowest two percent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place?
• If a light bulb has lasted seven years, what is the probability that it fails within the 8 th year?

Let T = the lifetime of a light bulb.

The decay parameter is m = 1/8, and T ∼ Exp(1/8). The cumulative distribution function is [latex]P\left(T

• Therefore, P ( T < 1) = 1 – e [latex]–\frac{1}{8}[/latex] ≈ 0.1175.

To do this, P (6 < t < 10) – P ( t < 6)

= [latex]=\left(1–{e}^{–\frac{1}{8}*10}\right)–\left(1–{e}^{–\frac{1}{8}*6}\right)[/latex] ≈ 0.7135 – 0.5276 = 0.1859

Solving for t , e [latex]–\frac{t}{8}[/latex] = 0.70, so [latex]–\frac{t}{8}[/latex] = ln (0.70), and t = –8 ln (0.70) ≈ 2.85 years.

Or use t = [latex]\frac{ln\text{(area_to_the_right)}}{\left(–m\right)}=\frac{ln\text{(0}\text{.70)}}{–\frac{1}{8}}\approx 2.\text{85 years}[/latex].

Solving for t , e [latex]–\frac{t}{8}[/latex] = 0.98, so [latex]–\frac{t}{8}[/latex] = ln (0.98), and t = –8 ln (0.98) ≈ 0.1616 years, or roughly two months.

The warranty should cover light bulbs that last less than 2 months.

Or use [latex]\frac{\ln(\text{area\_to\_the\_right})}{(-m)} = \frac{\ln(1-0.2)}{(-\frac{1}{8})}[/latex] = 0.1616.

Notice that by the rule of complement events, P ( T < 8| T > 7) = 1 – P ( T > 8| T > 7).

By the memoryless property ( P ( X > r + t | X > r ) = P ( X > t )).

So P ( T > 8| T > 7) = P ( T > 1) = [latex]1–\left(1–{e}^{–\frac{1}{8}}\right)={e}^{–\frac{1}{8}}\approx 0.8825[/latex]

Therefore, P ( T < 8| T > 7) = 1 – 0.8825 = 0.1175.

At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution.

• On average, how much time occurs between five consecutive calls?
• Find the probability that after a call is received, it takes more than three minutes for the next call to occur.
• Ninety percent of all calls occur within how many minutes of the previous call?
• Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute.
• Find the probability that less than 20 calls occur within an hour.

In major league baseball, a no-hitter is a game in which a pitcher, or pitchers, doesn’t give up any hits throughout the game. No-hitters occur at a rate of about three per season. Assume that the duration of time between no-hitters is exponential.

• What is the probability that an entire season elapses with a single no-hitter?
• If an entire season elapses without any no-hitters, what is the probability that there are no no-hitters in the following season?
• What is the probability that there are more than 3 no-hitters in a single season?

Let X = the number of no-hitters throughout a season. Since the duration of time between no-hitters is exponential, the number of no-hitters per season is Poisson with mean λ = 3.

Therefore, ( X = 0) = [latex]\frac{{3}^{0}{e}^{–3}}{0\text{!}}[/latex] = e –3 ≈ 0.0498

You could let T = duration of time between no-hitters. Since the time is exponential and there are 3 no-hitters per season, then the time between no-hitters is [latex]\frac{1}{3}[/latex] season. For the exponential, µ = [latex]\frac{1}{3}[/latex].

Therefore, m = [latex]\frac{1}{\mu }[/latex] = 3 and T ∼ Exp (3).

• The desired probability is P ( T > 1) = 1 – P ( T < 1) = 1 – (1 – e –3 ) = e –3 ≈ 0.0498.
• Let T = duration of time between no-hitters. We find P ( T > 2| T > 1), and by the memoryless property this is simply P ( T > 1), which we found to be 0.0498 in part a.
• Let X = the number of no-hitters is a season. Assume that X is Poisson with mean λ = 3. Then P ( X > 3) = 1 – P ( X ≤ 3) = 0.3528.

During the years 1998–2012, a total of 29 earthquakes of magnitude greater than 6.5 have occurred in Papua New Guinea. Assume that the time spent waiting between earthquakes is exponential.

• What is the probability that the next earthquake occurs within the next three months?
• Given that six months has passed without an earthquake in Papua New Guinea, what is the probability that the next three months will be free of earthquakes?
• What is the probability of zero earthquakes occurring in 2014?
• What is the probability that at least two earthquakes will occur in 2014?

According to the American Red Cross, about one out of nine people in the U.S. have Type B blood. Suppose the blood types of people arriving at a blood drive are independent. In this case, the number of Type B blood types that arrive roughly follows the Poisson distribution.

• If 100 people arrive, how many on average would be expected to have Type B blood?
• What is the probability that over 10 people out of these 100 have type B blood?
• What is the probability that more than 20 people arrive before a person with type B blood is found?
• [latex]\frac{100}{9}[/latex] = 11.11
• P ( X > 10) = 1 – P ( X ≤ 10) = 1 – Poissoncdf(11.11, 10) ≈ 0.5532.
• The number of people with Type B blood encountered roughly follows the Poisson distribution, so the number of people X who arrive between successive Type B arrivals is roughly exponential with mean μ = 9 and m = [latex]\frac{1}{9}[/latex]. The cumulative distribution function of X is [latex]P\left(X P ( X > 20) = 1 – P ( X ≤ 20) = [latex]1-\left(1-{e}^{-\frac{20}{9}}\right)\approx 0.1084.[/latex]

We could also deduce that each person arriving has a 8/9 chance of not having Type B blood. So the probability that none of the first 20 people arrive have Type B blood is [latex]{\left(\frac{8}{9}\right)}^{20}\approx 0.0948[/latex]. (The geometric distribution is more appropriate than the exponential because the number of people between Type B people is discrete instead of continuous.)

A web site experiences traffic during normal working hours at a rate of 12 visits per hour. Assume that the duration between visits has the exponential distribution.

• Find the probability that the duration between two successive visits to the website is more than ten minutes.
• The top 25% of durations between visits are at least how long?
• Suppose that 20 minutes have passed since the last visit to the web site. What is the probability that the next visit will occur within the next 5 minutes?
• Find the probability that less than 7 visits occur within a one-hour period.

At an urgent care facility, patients arrive at an average rate of one patient every seven minutes. Assume that the duration between arrivals is exponentially distributed.

• Find the probability that the time between two successive visits to the urgent care facility is less than 2 minutes.
• Find the probability that the time between two successive visits to the urgent care facility is more than 15 minutes.
• If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the next five minutes?
• Find the probability that more than eight patients arrive during a half-hour period.

Let T = duration (in minutes) between successive visits. Since patients arrive at a rate of one patient every seven minutes, μ = 7 and the decay constant is m = [latex]\frac{1}{7}[/latex]. The cdf is P ( T < t ) = [latex]1-{e}^{\frac{t}{7}}[/latex]

• P ( T < 2) = 1 – [latex]1-{e}^{-\frac{2}{7}}[/latex] ≈ 0.2485.
• P ( T > 15) = [latex]1-P\left(T15\right)=1-\left(1-{e}^{-\frac{15}{7}}\right)\approx {e}^{-\frac{15}{7}}\approx 0.1173[/latex].
• P ( T > 15| T > 10) = P ( T > 5) = [latex]1-\left(1-{e}^{-\frac{5}{7}}\right)={e}^{-\frac{5}{7}}\approx 0.4895[/latex].
• Let X = # of patients arriving during a half-hour period. Then X has the Poisson distribution with a mean of [latex]\frac{30}{7}[/latex], X ∼ Poisson[latex]\left(\frac{30}{7}\right)[/latex]. Find P ( X > 8) = 1 – P ( X ≤ 8) ≈ 0.0311.

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Unit 7: Probability

About this unit.

Probability tells us how often some event will happen after many repeated trials. You've experienced probability when you've flipped a coin, rolled some dice, or looked at a weather forecast. Go deeper with your understanding of probability as you learn about theoretical, experimental, and compound probability, and investigate permutations, combinations, and more!

Basic theoretical probability

• Intro to theoretical probability (Opens a modal)
• Probability: the basics (Opens a modal)
• Simple probability: yellow marble (Opens a modal)
• Simple probability: non-blue marble (Opens a modal)
• Intuitive sense of probabilities (Opens a modal)
• The Monty Hall problem (Opens a modal)
• Simple probability Get 5 of 7 questions to level up!
• Comparing probabilities Get 5 of 7 questions to level up!

Probability using sample spaces

• Example: All the ways you can flip a coin (Opens a modal)
• Die rolling probability (Opens a modal)
• Subsets of sample spaces (Opens a modal)
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Basic set operations

• Intersection and union of sets (Opens a modal)
• Relative complement or difference between sets (Opens a modal)
• Universal set and absolute complement (Opens a modal)
• Subset, strict subset, and superset (Opens a modal)
• Bringing the set operations together (Opens a modal)
• Basic set notation Get 5 of 7 questions to level up!

Experimental probability

• Experimental probability (Opens a modal)
• Theoretical and experimental probabilities (Opens a modal)
• Making predictions with probability (Opens a modal)
• Simulation and randomness: Random digit tables (Opens a modal)
• Experimental probability Get 5 of 7 questions to level up!
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Randomness, probability, and simulation

• Experimental versus theoretical probability simulation (Opens a modal)
• Theoretical and experimental probability: Coin flips and die rolls (Opens a modal)
• Random number list to run experiment (Opens a modal)
• Random numbers for experimental probability (Opens a modal)
• Statistical significance of experiment (Opens a modal)
• Interpret results of simulations Get 3 of 4 questions to level up!

Addition rule

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• Addition rule for probability (Opens a modal)
• Addition rule for probability (basic) (Opens a modal)
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• Two-way tables, Venn diagrams, and probability Get 3 of 4 questions to level up!

Multiplication rule for independent events

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Multiplication rule for dependent events

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Conditional probability and independence

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11 Surprising Homework Statistics, Facts & Data

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Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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The age-old question of whether homework is good or bad for students is unanswerable because there are so many “ it depends ” factors.

For example, it depends on the age of the child, the type of homework being assigned, and even the child’s needs.

There are also many conflicting reports on whether homework is good or bad. This is a topic that largely relies on data interpretation for the researcher to come to their conclusions.

To cut through some of the fog, below I’ve outlined some great homework statistics that can help us understand the effects of homework on children.

Homework Statistics List

1. 45% of parents think homework is too easy for their children.

A study by the Center for American Progress found that parents are almost twice as likely to believe their children’s homework is too easy than to disagree with that statement.

Here are the figures for math homework:

• 46% of parents think their child’s math homework is too easy.
• 25% of parents think their child’s math homework is not too easy.
• 29% of parents offered no opinion.

Here are the figures for language arts homework:

• 44% of parents think their child’s language arts homework is too easy.
• 28% of parents think their child’s language arts homework is not too easy.
• 28% of parents offered no opinion.

These findings are based on online surveys of 372 parents of school-aged children conducted in 2018.

2. 93% of Fourth Grade Children Worldwide are Assigned Homework

The prestigious worldwide math assessment Trends in International Maths and Science Study (TIMSS) took a survey of worldwide homework trends in 2007. Their study concluded that 93% of fourth-grade children are regularly assigned homework, while just 7% never or rarely have homework assigned.

3. 17% of Teens Regularly Miss Homework due to Lack of High-Speed Internet Access

A 2018 Pew Research poll of 743 US teens found that 17%, or almost 2 in every 5 students, regularly struggled to complete homework because they didn’t have reliable access to the internet.

This figure rose to 25% of Black American teens and 24% of teens whose families have an income of less than $30,000 per year.

4. Parents Spend 6.7 Hours Per Week on their Children’s Homework

A 2018 study of 27,500 parents around the world found that the average amount of time parents spend on homework with their child is 6.7 hours per week. Furthermore, 25% of parents spend more than 7 hours per week on their child’s homework.

American parents spend slightly below average at 6.2 hours per week, while Indian parents spend 12 hours per week and Japanese parents spend 2.6 hours per week.

5. Students in High-Performing High Schools Spend on Average 3.1 Hours per night Doing Homework

A study by Galloway, Conner & Pope (2013) conducted a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California. 

Across these high-performing schools, students self-reported that they did 3.1 hours per night of homework.

Graduates from those schools also ended up going on to college 93% of the time.

6. One to Two Hours is the Optimal Duration for Homework

A 2012 peer-reviewed study in the High School Journal found that students who conducted between one and two hours achieved higher results in tests than any other group.

However, the authors were quick to highlight that this “t is an oversimplification of a much more complex problem.” I’m inclined to agree. The greater variable is likely the quality of the homework than time spent on it.

Nevertheless, one result was unequivocal: that some homework is better than none at all : “students who complete any amount of homework earn higher test scores than their peers who do not complete homework.”

7. 74% of Teens cite Homework as a Source of Stress

A study by the Better Sleep Council found that homework is a source of stress for 74% of students. Only school grades, at 75%, rated higher in the study.

That figure rises for girls, with 80% of girls citing homework as a source of stress.

Similarly, the study by Galloway, Conner & Pope (2013) found that 56% of students cite homework as a “primary stressor” in their lives.

8. US Teens Spend more than 15 Hours per Week on Homework

The same study by the Better Sleep Council also found that US teens spend over 2 hours per school night on homework, and overall this added up to over 15 hours per week.

Surprisingly, 4% of US teens say they do more than 6 hours of homework per night. That’s almost as much homework as there are hours in the school day.

The only activity that teens self-reported as doing more than homework was engaging in electronics, which included using phones, playing video games, and watching TV.

9. The 10-Minute Rule

The National Education Association (USA) endorses the concept of doing 10 minutes of homework per night per grade.

For example, if you are in 3rd grade, you should do 30 minutes of homework per night. If you are in 4th grade, you should do 40 minutes of homework per night.

However, this ‘rule’ appears not to be based in sound research. Nevertheless, it is true that homework benefits (no matter the quality of the homework) will likely wane after 2 hours (120 minutes) per night, which would be the NEA guidelines’ peak in grade 12.

10. 21.9% of Parents are Too Busy for their Children’s Homework

An online poll of nearly 300 parents found that 21.9% are too busy to review their children’s homework. On top of this, 31.6% of parents do not look at their children’s homework because their children do not want their help. For these parents, their children’s unwillingness to accept their support is a key source of frustration.

11. 46.5% of Parents find Homework too Hard

The same online poll of parents of children from grades 1 to 12 also found that many parents struggle to help their children with homework because parents find it confusing themselves. Unfortunately, the study did not ask the age of the students so more data is required here to get a full picture of the issue.

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Interpreting the Data

Unfortunately, homework is one of those topics that can be interpreted by different people pursuing differing agendas. All studies of homework have a wide range of variables, such as:

• What age were the children in the study?
• What was the homework they were assigned?
• What tools were available to them?
• What were the cultural attitudes to homework and how did they impact the study?
• Is the study replicable?

The more questions we ask about the data, the more we realize that it’s hard to come to firm conclusions about the pros and cons of homework .

Furthermore, questions about the opportunity cost of homework remain. Even if homework is good for children’s test scores, is it worthwhile if the children consequently do less exercise or experience more stress?

Thus, this ends up becoming a largely qualitative exercise. If parents and teachers zoom in on an individual child’s needs, they’ll be able to more effectively understand how much homework a child needs as well as the type of homework they should be assigned.

Related: Funny Homework Excuses

The debate over whether homework should be banned will not be resolved with these homework statistics. But, these facts and figures can help you to pursue a position in a school debate on the topic – and with that, I hope your debate goes well and you develop some great debating skills!

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd-2/ 25 Study Desk Aesthetic Ideas
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1.1 Definitions of Statistics, Probability, and Key Terms

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A politician is interested in the proportion of voters in his district who think he is doing a good job.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

A marketing company is interested in the proportion of people who will buy a particular product.

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following:

X X = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

• population.

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of a:

1.2 Data, Sampling, and Variation in Data and Sampling

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

percent of body fat

favorite baseball team

time in line to buy groceries

number of students enrolled at Evergreen Valley College

most-watched television show

brand of toothpaste

distance to the closest movie theatre

age of executives in Fortune 500 companies

number of competing computer spreadsheet software packages

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

“Number of times per week” is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

“Duration (amount of time)” is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a telephone survey.

List some practical difficulties involved in getting accurate results from a mailed survey.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

• simple random

Name the sampling method used in each of the following situations:

• A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
• A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
• The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
• The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
• A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

A “random survey” was conducted of 3,274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?
• Based on your “gut feeling,” do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called “America’s Smithsonian.”
• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, George Gallup conducted his own poll of 30,000 prospective voters. These researchers used a method they called "quota sampling" to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in 1.2 Data, Sampling, and Variation in Data and Sampling could explain this connection?

YouPolls is a website that allows anyone to create and respond to polls. One question posted April 15 asks:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” (lastbaldeagle. 2013. On Tax Day, House to Call for Firing Federal Workers Who Owe Back Taxes. Opinion poll posted online at: http://www.youpolls.com/details.aspx?id=12328 (accessed May 1, 2013).)

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.”(Scott Keeter et al., “Gauging the Impact of Growing Nonresponse on Estimates from a National RDD Telephone Survey,” Public Opinion Quarterly 70 no. 5 (2006), http://poq.oxfordjournals.org/content/70/5/759.full (accessed May 1, 2013).)

The Pew Research Center for People and the Press admits:

“The percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.” (Frequently Asked Questions, Pew Research Center for the People & the Press, http://www.people-press.org/methodology/frequently-asked-questions/#dont-you-have-trouble-getting-people-to-answer-your-polls (accessed May 1, 2013).)

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

1.3 Frequency, Frequency Tables, and Levels of Measurement

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

• Fill in the blanks in Table 1.33 .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.34 .

• Fill in the blanks in Table 1.34 .
• What percent of adults flossed six times per week?
• What percent flossed at most three times per week?

Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 ; 5 ; 7 ; 2 ; 2 ; 10 ; 20 ; 15 ; 0 ; 7 ; 0 ; 20 ; 5 ; 12 ; 15 ; 12 ; 4 ; 5 ; 10 .

Table 1.35 was produced.

• Fix the errors in Table 1.35 . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the U.S. five or seven years?
• What fraction of the people surveyed have lived in the U.S. at most 12 years?
• What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
• What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?

How much time does it take to travel to work? Table 1.36 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. Table 1.37 shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

Use the following information to answer the next two exercises: Table 1.38 contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• Not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

1.4 Experimental Design and Ethics

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

An advertisement for Acme Investments displays the two graphs in Figure 1.14 to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

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Access for free at https://openstax.org/books/introductory-statistics/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Introductory Statistics
• Publication date: Sep 19, 2013
• Location: Houston, Texas
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• N5 Maths Topics
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Let the fantastic wealth of resources below teach you all about Statistics.

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Covers the whole of the National 5 Maths course

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Resources used with students studying Maths in Scottish Secondary Schools

Welcome to  national5maths.co.uk

A sound understanding of  Statistics  is essential to ensure exam success.

Passing N5 Maths significantly increases your career opportunities by helping you gain a place on a college course, apprenticeship or even landing a job. A ‘good’ pass at N5 Maths will set you up well for the fast paced  Higher Maths Course  next year should you be interested. Please do your very best to keep on top of your studies.

For students looking for extra help with the N5 Maths course you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack .

To access a wealth of additional  free resources by topic  please either use the above  Search Bar  or click  HERE  selecting on the topic you wish to study.

We hope the resources on this website prove useful and wish you the very best of success with your N5 Maths course in 2025. Please find below:

1. Standard Deviation & Statistics – Worksheets

2. About Statistics

3. Statistics – Videos, PowerPoints & Mind Maps

4. N5 Maths Essential Skills  

5. N5 Maths Exam Worksheets by Topic

6. Credit Maths Exam Worksheets by Topic

7. N5 Maths Exam Questions & Answers by Topic 

8. N5 Maths 180 Booster Papers   

9. N5 Maths Videos, PowerPoints, Mind Maps & Worksheets

10. N5 Maths SQA Past & Practice Papers

11. 100 N5 Maths Exam Questions & Answers

12. N5 Maths Exam Check Lists

13. N5 Maths Exam Focused Homework

14. N5 Maths Prelim Practice

15. N5 Maths Further Revision Practice

16. Credit & Int 2 Maths SQA Papers

17. 100 N5 Maths Lesson Starter Questions 

18. N5 Maths – Applications Unit Practice Assessment

19. N5 Maths – Expressions & Formulae Unit Practice Assessment

20. N5 Maths – Relationships Unit Practice Assessment

21. N5 Maths Mind Maps

22. N5 Maths PowerPoints

23. Maths Websites (Including Games/Puzzles)

24. Recommended National 5 Maths Books

25. N5 Maths Online Study Pack  – Students looking for a ‘good’ Pass

National 5 Maths Resources

1.  Standard Deviation & Statistics – Worksheets

Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam. Clear, easy to follow, step-by-step worked solutions to the Essential Skills worksheet and N5 Maths exam questions below are available in the  Online Study Pack.

. 2. About Statistics

To learn about Statistics please click on the Statistics Theory link. Please also find in Sections 2 & 3 below videos, PowerPoints, mind maps and worksheets on this topic to help your understanding. The Essential Skills 12 worksheet, along with actual  SQA Exam Questions , are highly recommended.

If you would like more help understanding Statistics there are clear, easy to follow, step-by-step worked solutions to dozens of N5 Maths Past & Practice exam questions on all topics in the Online Study Pack. Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack  today.

Statistics are:

• A set of data collected in a scientific, unbiased and methodical way to provide information on a set of events happening repeatedly. 
• Widely used in many professions such as Forensics, Government Statistician, Actuarists and even people who predict the weather!

Topics covered include:

Quartiles & Averages

Here a data set is placed in order and divided into 4 groups in order to find the quartiles Q1, Q2 & Q3 . From the quartiles a box plot can be drawn to give a 5 Figure Summary pictorial representation.

• Standard Deviation

Standard deviation is important in finding how much variance there is from the mean and is a reliable measure of spread since all the statistics are used in its calculation.

• Scatter Graphs

Scatter graphs are a type of mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

They are pictorial representations of large sets of numbers displaying useful information such as the lowest & highest data points, median and spread.

A Dot Chart or Dot Plot is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

3. Statistics – Videos, PowerPoints & Mind Maps  

Thanks to the authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.

Thanks to Mr G Rennie for making the excellent resources below freely available. The Essential Skills Worksheets can be used for general revision, homework, consolidation of a topic or preparation for assessments, tests and exams. Clear, easy to follow, step-by-step worked solutions to all 30 Essential Skills worksheets are available in the  Online Study Pack.

5. N5 Maths Exam Worksheets by Topic 

Thanks to the SQA and authors for making the excellent resources below freely available. The worksheets by topic below are a fantastic study resource since they are actual SQA past paper exam questions. Clear, easy to follow, step-by-step worked solutions to all SQA N5 Maths Questions below are available in the  Online Study Pack.

. 6. Credit Maths Exam Worksheets by Topic

Thanks to the SQA and authors for making the excellent resources below freely available. In 2015 N5 Maths replaced  Credit Maths . The Credit worksheets by topic below are a fantastic additional study resource.

Thanks to the SQA and authors for making the excellent resources below freely available. Questions & answers have been split up by topic for your ease of reference. Clear, easy to follow, step-by-step worked solutions to all N5 Maths Questions below are available in the  Online Study Pack.

. 8. N5 Maths 180 Booster Papers

Thanks to maths180.com for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.

Dozens of N5 Maths Videos, PowerPoints and Mind Maps provide quality lessons by topic. Also included are excellent revision worksheets, with actual SQA N5 Maths exam questions, to aid your understanding.   Please click on our  N5 Maths Videos & Worksheets  dedicated page.

10. N5 Maths SQA Past & Practice Papers 

Thanks to the SQA and maths180.com for making the excellent resources below freely available. Clear, easy to follow, step-by-step worked solutions to all sixteen N5 Maths Past & Practice Papers below are available in the  Online Study Pack.

11. 100 N5 Maths Exam Type Questions & Answers 

Thanks to the SQA and authors for making the excellent resources below freely available. Please try to do as many questions as possible, checking your answers as you go. If stuck, always ask your teacher for help as soon as possible. Clear, easy to follow, step-by-step worked solutions to all 100 N5 Maths Questions below are available in the Online Study Pack.

12. N5 Maths Exam Check Lists 

Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.

Thanks to the SQA and authors for making the excellent resources below freely available. The exercises below are a fantastic resource which can also be used for revision prior to assessments, tests and the final exam.

14. N5 Maths Prelim  Practice 

Thanks to the SQA and authors for making the excellent resources below freely available. Please use the below for revision prior to assessments, tests and the final exam.

15. N5 Maths Further Revision  Practice 

The excellent resources below are courtesy of Larkhall Academy. Please use the below for revision prior to assessments, tests and the final exam.

Thanks to the SQA for making the excellent resources below freely available. The SQA Past Papers below are a fantastic additional study resource.

17. 100 N5 Maths Lesson Starters

Thanks to the authors for making the excellent resources below freely available.

The start of the lesson is important for setting the tone. This is the time during the lesson for practising, revisiting and developing further those aspects of mathematics which need a ‘little but often’ approach. Additional Lesson Starters for S1 & S2 can be found by clicking on the Free S1 & S2  Home Page  HERE . 

18. N5 Maths – Applications Unit Practice Assessment 

19. N5 Maths – Expressions & Formulae Unit Practice Assessment 

Thanks to the authors for making these freely available. Mind Maps are an excellent diagrammatic way of organising key ideas or concepts from lessons/text books.

22. N5 Maths PowerPoints 

24. Recommended N5 Maths Books

The highly recommended National 5 Maths books below can be used with students to compliment the material on this website. Click on the links below and order both books through amazon.co.uk.

TJ N5 Maths Text Book

This above can be used as a free-standing National 5 book for students, possibly in Secondary 4, 5 or 6, who have previously successfully completed a CfE Level 4 course, or equivalent.

• TeeJay’s usual bight colourful pupil centred Textbook.
• Each exercise is graded with the more problematic questions at the end.
• National 5 Outcomes listed for easy reference
• Contains a Chapter Zero that Revises the contents of TeeJays CfE 4+ Book.
• Six Cumulative Home Exercises interspersed throughout the book.
• Six Non Calculator Exercises throughout the book.
• Each Chapter ends with a “Remember Remember” exercise as a summary.
• The book ends with a Revision Chapter, consolidating the whole of the National 5 Course.
• Contains a National 5 Specimen Paper 1 and Paper 2.

N5 Maths Success Guide

National 5 Mathematics Success Guide provides easy-to-use and value-for-money revision for all abilities and learning styles. Guidance on how the new National 5 course and assessments are structured is included. All the popular features of this tried and trusted series are retained in the new National 5 Guides.

• Colourful double-page spreads aid both comprehensive and revision planning • Topics are broken down into small, easily managed sections, complemented with lots of diagrams and illustrations to aid retention • Quick Tests and Top Tips help keep students focused on the exam’s precise demands • Revision checklists help students to manage and track their progress in the lead up to the exam • A glossary present all of the key terms and definitions essential for the exam

25. National 5 Maths Online Study Pack

Through step-by-step worked solutions to exam questions available in the Online Study Pack we cover everything you need to know about  Statistics to pass your final exam.

For students looking for a ‘good’ pass at N5 Maths you may wish to consider subscribing to the fantastic additional exam focused resources available in the Online Study Pack. Subscribing could end up being one of your best ever investments.

Please give yourself every opportunity for success, speak with your parents, and subscribe to the exam focused Online Study Pack  today.

We hope you find this website useful and wish you the very best of success with N5 Maths in 2025.

6 different ways for you to study Statistics

N5 Maths Study Pack

Click on the link below to purchase the Online N5 Maths Study Pack

Higher Maths Website

Click on the link below to visit the Higher Maths website

AH Maths Website

Click on the link below to visit the AH Maths website

• N5 Applications of Maths

Click on the link below to visit the N5 Applications of Maths homepage

S1 & S2 Maths

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E-mailing you guys know that you are doing a great job compiling all these excellent resources, it has been a great help to me and probably many many others. It has allowed me to get a reassuring prelim mark and has given me confidence for the final exam ( tomorrow ). Thanks for all the help and keep up the good work.

Hello, I decided to write to you to thank you for this website, it has helped me incredibly and the amount of content you have is amazing. I was very happy to discover the many practice papers you have as I had began to run out of papers to do once completed all the SQA past papers. The checklists for the three different units is very helpful and I will definitely be taking these to school with me on the day of my exam to look over! Thank you again for being so helpful to us, it is greatly appreciated and I will be placing any success I have during the National 5 exam on this website due to the endless resources and help you have available. Thank you 🙂 Emily, Nat 5 Maths student.

It is a great help to us this site, my daughter scored 86% in her prelim after doing the last 5 years past papers

Hi there – we found your site an amazing help for nat 5 – in fact my son went from a C grade at prelim to an A for his nat 5 thanks to you.  Thank you – the best £20 I’ve spent!

Ms McCallum

“My Dad and I have worked together through several topics and three Practice Past Papers. When I get stuck, the detailed worked solutions explain everything so clearly and even give alternative ways to find the correct answer –  Thank you so much for producing this fantastic resource.”

Darcey, Secondary School Maths Student

“Just want to say what a fantastic resource this is.

An absolute godsend for my Nat 4  and Nat 5 classes.

Many thanks”.

Mr Wilson, Teacher of Mathematics, Edinburgh

“The website is great!! It is very easy to navigate through and it has helped me understand many of the topics I was previously struggling with.”

Dean, Secondary School Maths student

“The website is really easy to follow and has absolutely everything you need to pass.”

Cameron, Secondary School Maths student

“Everything about my Maths course is here on this fantastic website. I use the study guides all the time to help my classroom learning as everything is explained so clearly – I have no excuses so it is all down to me now!”

Ben, Secondary School Maths Student

“I’d highly recommend this maths website to all parents wishing the best for their son or daughter. The clarity in which the topics have been explained through the study guides are simply first class.”

Mr W, Mathematics Teacher

“Hi, I am in my second year at Abertay University studying Forensics. Two years ago, while studying N5 Maths, my Maths teacher helped me realise my dreams by providing me with all the superb material which is now available on this website. With the right intention to study, everything is here for you to pass National 5 Maths”

Ross, former National 5 Maths student

“This material is quite the best that I’ve discovered. It helps students to focus on one subject at a time, gaining confidence as they work through the revision guides and self check booklets.”

Mr D, Mathematics Teacher

“The simplified methods in the study guides are easy to follow. I feel that I have progressed enormously with my Maths and I would encourage all pupils who are struggling to go onto this website as soon as possible.”

Marc, Secondary School Maths Student

“I am studying Maths at College since it a requirement for me to train to become a primary school teacher. I am delighted to have found this website and make my life long dream of becoming a teacher a reality!”

Sharon, Mature Maths Student

“I am studying GCSE Maths at College as I am hoping to go to University to study Accountancy. This website is just amazing!! I regularly refer to the Theory Guides to help me understand topics I am struggling with. The worked solutions in the Online Study Pack are also fantastic as it teaches me the correct way to lay out my working and, at the same time, check my answers.”

Hollie, Mature Maths Student

“Although I am only in 3rd year we are working at National 5 level maths and have a Unit Assessment in the next few weeks. I really want to study Computer Games Development at University which requires me to pass Maths so I am studying hard now. The website is helping me so much.”

Oliver, Secondary School Maths Student

“The website is really good as it breaks the whole course down into easy to understand sections. I need to get A-Level Maths next year as I want to go to university and study engineering. I am really glad to have found this website to help me on my way.”

Salim, Secondary School Maths Student

Not just Statistics, but 70 other maths concepts covered in detail

Topic Links

Free resources to dozens of National 5 Maths topics are available by clicking on any of the links to the right.

• N5 Maths Whole Course
• N5 Maths Past Papers
• N5 Past Papers by Topic
• N5 Revision Check Lists
• N5 Maths Booster Papers
• N5 Maths Essential Skills
• N5 Maths Theory Guides
• N5 Maths Mind Maps
• N5 Maths Videos
• N5 Maths Assessments
• N5 Maths Numeracy Unit
• All Maths Courses
• Algebraic Fractions
• Angles & Shapes
• Arcs & Sectors
• Applications Assessment
• Area of a Triangle
• CAST Diagram
• Changing the Subject
• Codebreaker Worksheets
• Completing the Square
• Compound Interest
• Constructing Formulae
• Converse of Pythagoras
• Correlation
• Cosine Rule
• Difference of Two Squares
• Discriminant
• Expressions & Formulae
• Factorisation
• Factorising Trinomials
• Growth Mindset Booklets
• Higher Maths
• Inequalities
• Linear Relationships
• Maths Websites
• N5 & Higher Maths Tuition
• Nature of the Roots
• Numeracy & Maths
• Percentages
• Probability
• Quadratic Equations
• Quadratic Functions
• Quadratic Formula
• Quadratic Graphs
• Rationalising Denominator
• Relationships Assessment
• Reversing a % Change
• S1 & S2 Maths
• Scientific Notation
• Significant Figures
• Similar Figures
• Simultaneous Equations
• SOH-CAH-TOA
• Straight Lines
• Trigonometry
• Trig Equations
• Trig Graphs
• Trig Identities
• Vector Addition
• Vector Components
• Vector Magnitude
• Vector Pathways
• Vectors & Scalars
• Vector Subtraction
• Vectors 3-D
• Vectors & Coords 3-D

For Students

To ensure your success in 2024/25 there is a wealth of fantastic additional N5 Maths exam focused resources for less than the cost of a text book.

Just £20 for a year

Buy now >

For Schools

Schools can get the Online Study Pack also. Unlimited use for all the teachers and students in your school.

Just £200 for a year

• Subject list

This fantastic Maths resource was set up by a practicing secondary high school maths teacher.

To read more about the story behind the site, please click here .

Get in touch

We wish you the very best of success in 2024/25.

For any questions, please e-mail us at the address below.

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