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Theoretical vs. Experimental Probability: How do they differ?

Probability is the study of chances and is an important topic in mathematics. There are two types of probability: theoretical and experimental.

So, how to define theoretical and experimental probability? Theoretical probability is calculated using mathematical formulas, while experimental probability is based on results from experiments or surveys. In order words, theoretical probability represents how likely an event is to happen. On the other hand, experimental probability illustrates how frequently an event occurs in an experiment.

Read on to find out the differences between theoretical and experimental probability. If you wonder How to Understand Statistics Easily , I wrote a whole article where I share 9 helpful tips to help you Ace statistics.

Table of Contents

What Is Theoretical Probability?

Theoretical probability is calculated using mathematical formulas. In other words, a theoretical probability is a probability that is determined based on reasoning. It does not require any experiments to be conducted. Theoretical probability can be used to calculate the likelihood of an event occurring before it happens.

Keep in mind that theoretical probability doesn’t involve any experiments or surveys; instead, it relies on known information to calculate the chances of something happening.

For example, if you wanted to calculate the probability of flipping a coin and getting tails, you would use the formula for theoretical probability. You know that there are two possible outcomes—heads or tails—and that each outcome is equally likely, so you would calculate the probability as follows: 1/2, or 50%.

How Do You Calculate Theoretical Probability?

• First, start by counting the number of possible outcomes of the event.
• Second, count the number of desirable (favorable) outcomes of the event.
• Third, divide the number of desirable (favorable) outcomes by the number of possible outcomes.
• Finally, express this probability as a decimal or percentage.

The theoretical probability formula is defined as follows: Theoretical Probability = Number of favorable (desirable) outcomes divided by the Number of possible outcomes.

How Is Theoretical Probability Used in Real Life?

Probability plays a vital role in the day to day life. Here is how theoretical probability is used in real life: 

• Sports and gaming strategies
• Analyzing political strategies.
• Buying or selling insurance
• Determining blood groups 
• Online shopping
• Weather forecast
• Online games

What Is Experimental Probability?

Experimental probability, on the other hand, is based on results from experiments or surveys. It is the ratio of the number of successful trials divided by the total number of trials conducted. Experimental probability can be used to calculate the likelihood of an event occurring after it happens.

For example, if you flipped a coin 20 times and got heads eight times, the experimental probability of obtaining heads would be 8/20, which is the same as 2/5, 0.4, or 40%.

How Do You Calculate Experimental Probability?

The formula for the experimental probability is as follows:  Probability of an Event P(E) = Number of times an event happens divided by the Total Number of trials .

If you are interested in learning how to calculate experimental probability, I encourage you to watch the video below.

How Is Experimental Probability Used in Real Life?

Knowing experimental probability in real life provides powerful insights into probability’s nature. Here are a few examples of how experimental probability is used in real life:

• Rolling dice
• Selecting playing cards from a deck
• Drawing marbles from a hat
• Tossing coins

The main difference between theoretical and experimental probability is that theoretical probability expresses how likely an event is to occur, while experimental probability characterizes how frequently an event occurs in an experiment.

In general, the theoretical probability is more reliable than experimental because it doesn’t rely on a limited sample size; however, experimental probability can still give you a good idea of the chances of something happening.

The reason is that the theoretical probability of an event will invariably be the same, whereas the experimental probability is typically affected by chance; therefore, it can be different for different experiments.

Also, generally, the more trials you carry out, the more times you flip a coin, and the closer the experimental probability is likely to be to its theoretical probability.

Also, note that theoretical probability is calculated using mathematical formulas, while experimental probability is found by conducting experiments.

What to read next:

• Types of Statistics in Mathematics And Their Applications .
• Is Statistics Harder Than Algebra? (Let’s find out!)
• Should You Take Statistics or Calculus in High School?
• Is Statistics Hard in High School? (Yes, here’s why!)

Wrapping Up

Theoretical and experimental probabilities are two ways of calculating the likelihood of an event occurring. Theoretical probability uses mathematical formulas, while experimental probability uses data from experiments. Both types of probability are useful in different situations.

I believe that both theoretical and experimental probabilities are important in mathematics. Theoretical probability uses mathematical formulas to calculate chances, while experimental probability relies on results from experiments or surveys.

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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Theoretical Probability versus Experimental Probability

You've heard the terms, theoretical probability and experimental probability , but what do they mean?

Are they in anyway related? This is what we are going to discover in this lesson.

If you've completed the lessons on i ndependent and dependent probability , then you've already found the theoretical probability for numerous problems.

Theoretical Probability

Theoretical probability is the probability that is calculated using math formulas. This is the probability based on math theory.

Experimental Probability

Experimental probability is calculated when the actual situation or problem is performed as an experiment. In this case, you would perform the experiment, and use the actual results to determine the probability.

In order to accurately perform an experiment, you must:

• Identify what constitutes a " trial ".
• Perform a minimum of 25 trials
• Set up an organizer (table or chart) to record your data.

Let's take a look at an example where we first calculate the theoretical probability, and then perform the experiment to determine the experimental probability.

It will be interesting to compare the theoretical probability and the experimental probability. Do you think the two calculations will be close?

Example 1 - Theoretical Versus Experimental

This problem is from Example 1 in the  independent events  lesson. We calculated the theoretical probability to be 1/12 or 8.3%. Take a look:

Since we know that the theoretical probability is 8.3% chance of flipping a head and rolling a 6, let's see what happens when we actually perform the experiment.

Identify a trial: A trial consists of flipping a coin once and rolling a die once.

Conduct 25 trials and record your data in the table below.

For each trial, I flipped the coin once and rolled the die. I recorded and H for heads and a T for tails in the row labeled "Coin."

I recorded the number on the die in the row labeled "Die".

In the last row I determined whether the trial completed the event of flipping a head and rolling a six.

In this experiment, there was only 1 trial (out of 25) where a head was flipped on the coin and a 6 was rolled on the die.

This means that the experimental probability is 1/25 or 4%.

Please note that everyone's experiment will be different; thus allowing the experimental probability to differ.

Also, the more trials that you conduct in your experiment, the closer your calculations will be for the experimental and theoretical probabilities.

Conclusions

The theoretical probability is 8.3% and the experimental probability is 4%. Although the experimental probability is slightly lower, this is not a significant difference.

In most experiments, the theoretical probability and experimental probability will not be equal; however, they should be relatively close.

If the calculations are not close, then there's a possibility that the experiment was conducted improperly or more trials need to be completed.

I hope this helps to give you a sense of how to set up an experiment in order to compare theoretical versus experimental probabilities.

• Probability
• Theoretical/Experimental Probability

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Experimental vs Theoretical Probability: Difference and Comparison

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An experiment can have several possibilities while listing many circumstances, although there are two types of probabilities – Experimental and Theoretical Probability. The term probability is a common term in maths.

Probability lists out events to observe what is likely to happen in an experiment without or after performing an experiment. In other words, it is the prospect of an event happening. 

Key Takeaways Experimental probability is based on the observed outcomes of an experiment, while theoretical probability relies on mathematical analysis. Experimental probability can change with each trial, whereas theoretical probability remains constant. Theoretical probability assumes a fair and unbiased sample space, while experimental probability depends on an experiment’s specific conditions and results.

Experimental vs Theoretical Probability

Experimental probability is a probably based on possible outcomes arrived after gathering information through experiments. The result of the experiment gives the chances of an event happening. Theoretical probability is the possibility of an event happening without an experiment, so it is assumption-based.

Experimental probability is a probability based on possible outcomes after gathering information by experimenting. In other words, the chances of happening an event by gathering information or collecting data by experimenting.

Its foundation is on what happened during an event. And the formula is the ratio of possible outcomes of a specific event to the total number of trials. 

Theoretical probability is the possibility of an event happening without experimenting. Also, its foundation is assumption-based. In this probability, the experiment does not follow.

However, assumptions are taken into consideration to find a certain probability of an event. And the formula is the ratio of the number of suitable outcomes to the number of plausible outcomes.

Comparison Table

What is Experimental Probability? 

Experimental Probability is the probability of the occurrence of a specific event based on an experiment.  It is also known as empirical probability. 

Experimental probability is based on outcomes gathered by repeatedly experimenting. Moreover, it focuses on what happened during an experiment rather than what would happen. 

Some specific outcomes are gathered before determining a certain event’s probability. Besides, an experiment is conducted repeatedly to collect desired outcomes.

Its basic approach differs from theoretical probability, although both find probability. 

Probability based on data and experiment results is reliable as it’s more likely to happen than assumption-based probability.

However, both have their pros and cons. A probability is just a prediction of what is likely to happen in the future. So, it may result in an unexpected outcome. 

Although, an experimental-based probability is more likely to happen due to the greater number of outcomes that lead closer to happening an event.

As we already know, that experimental probability is more reliable.

But, many factors affect the results of an event in many situations, such as batting averages, shooting percentage, and other similar data from sports; predicting the weather, sales figure of a movie or series; polls and surveys that collect opinions; and historical data. 

Coming to the formula the formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials. 

What is Theoretical Probability?

Theoretical Probability is the probability of the possibility of a specific event based on an assumption without actually experimenting. It is the theory behind probability. 

For theoretical probability, knowing about an event is necessary rather than experimenting. The chances of happening a specific event are considered rather than actual outcomes.

Moreover, it predicts what will happen in the future based on the possibility of an event. 

It accounts for favourable outcomes for further prediction of the possibility of an event. Rather than relying on data and experiment results, it depends on assumed data.  The approaches of both probabilities are different from each other. 

Its approach is to predict the outcomes without actually performing an event. 

Moreover, it is not considered as reliable as an experimental probability because it does not acknowledge facts and perform an experiment. Although, both probabilities can be proven wrong as other factors affect situations and change the result at last. 

However, it is considered reliable in certain situations, such as a physical relationship based on theoretical probability where the object involved in an event can be seen, measurable, and does not change over time.

It includes coin flippers, spinners, several coins, etc.  

Lastly, the fourth formula is the ratio of the number of suitable outcomes to the number of plausible outcomes.

Main Differences Between Experimental and Theoretical Probability

Probability is the chance of an event happening with or without experimenting. Its ideal approach is to predict what will happen in the future. But, seldom do certain factors affect an event, and the result of an experiment can change drastically.  

There are two types of probabilities – Experimental and Theoretical probability. Both are reliable, yet in different circumstances. 

• Experimental probability is the possibility of a particular event happening with experimenting. Meanwhile, the theoretical probability is the possibility of a particular 
• In experimental probability, an experiment is performed. While the theoretical probability, an experiment does not.
• In experimental probability, the data is gathered by experimenting repeatedly. While in theoretical probability, the data is collected by considering every possible outcome that has a chance to happen during an experiment without actually performing it. 
• In experimental probability, outcomes gathered through the experiment are considered for finding the possibility of an event. Meanwhile, theoretical probability considers outcomes that are likely to happen. 
• In experimental probability, its approach is based on what has happened, while, in the theoretical experiment, its approach is based on what would happen considered possible outcomes.
• Experimental probability is reliable in batting averages, shooting percentages, and other similar data from sports; predicting the weather, sales figure of a movie or series; polls and surveys that collect opinions; and historical data. While the theoretical probability is reliable in a kind of probability based on a physical relationship where objects involved can be seen, measurable, and doesn’t change over time. 
•  The experimental probability it’s based on data and facts. In contrast, the theoretical probability it’s based on assumption. 
• The formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials. In comparison, the formula of theoretical probability is the ratio of the number of suitable outcomes to the number of plausible outcomes.
• https://link.springer.com/content/pdf/10.1007/s11858-012-0469-z.pdf
• https://www.iejme.com/article/building-a-connection-between-experimental-and-theoretical-aspects-of-probability

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Home / United States / Math Classes / 7th Grade Math / Experimental and Theoretical Probability

Experimental and Theoretical Probability

Probability is a branch of math that studies the chance or likelihood of an event occurring. There are two types of prob ability for a particular event: experimental probability and theoretical probability. Learn the difference between the two types of probabilities and the steps involved in their calculation. ...Read More Read Less

Experimental and Theoretical Probability in Math

What is Probability?

• Experimental Probability
• Theoretical Probability
• Solved Examples
• Frequently Asked Questions

Th e chance of a happening is named as the probability of the event happening. It tells us how likely an occasion is going to happen; it doesn’t tell us what’s happening. There is a fair chance of it happening (happening/not happening). They’ll be written as decimals or fractions . The probability of occurrence A is below.

P (A) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of total possible outcomes}}\)

Following are two varieties of probability:

• Experimental probability
• Theoretical probability

What is Experimental Probability

Definition : Probability that’s supported by repeated trials of an experiment is named as experimental probability.

P (event) = \(\frac{\text{Number of times that event occurs}}{\text{Total number of trails}}\)

Example: The table shows the results of spinning a penny 62 times. What’s the probability of spinning heads?

Solution: Heads were spun 23 times in a total of 23 + 39 = 62 spins.

P (heads) = \(\frac{\text{23}}{\text{69}}\) = 0.37  or 37.09 %

What is Theoretical Probability

Definition : When all possible outcomes are equally likely the theoretical possibility of an incident is that the quotient of the number of favorable outcomes and therefore the number of possible outcomes.

P (event) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\)

Example: You randomly choose one among the letters shown. What’s the theoretical probability of randomly choosing an X?

Solution: P (x) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\) = \(\frac{\text{1}}{\text{7}}\) or 14.28%

A prediction could be a reasonable guess about what is going to happen in the future. Good predictions should be supported by facts and probability.

Predictions supported theoretical probability. These are the foremost reliable varieties of predictions, based on physical relationships that are easy to work and measure which don’t change over time. They include such things as:

• number cubes

Let’s take a look at some differences between experimental and theoretical probability:

Theoretical & Experimental Probability Examples

1. What is the probability of tossing a variety cube and having it come up as a two or a three?

Solution:  

First, find the full number of outcomes

Outcomes: 1, 2, 3, 4, 5, and 6

Total outcomes = 6

Next, find the quantity of favorable outcomes.

Favorable outcomes:

Getting a 2 or a 3 = 2 favorable outcomes

Then, find the ratio of favorable outcomes to total outcomes.

P (Event) = Number of favorable outcomes : total number of outcomes

P (2 or 3) = 2:6

P (2 or 3) = 1:3

The solution is 1:3

The theoretical probability of rolling a 2 or a 3 on a variety of cube is 1:3.

2 . A bag contains 25 marbles. You randomly draw a marble from the bag, record its color, so replace it. The table shows the results after 11 draws. Predict the amount of red marbles within the bag.

To seek out the experimental probability of drawing a red marble.

P (EVENT) = \(\frac{\text{Number of times the event occurs}}{\text{Total number of trials}}\)

P (RED) = \(\frac{\text{5}}{\text{11}}\)        (You draw red 5 times. You draw a complete of 11 marbles)

To make a prediction, multiply the probability of drawing red by the overall number of marbles within the bag.

\(\frac{\text{5}}{\text{11}}\) x 25 = 11.36 ~ 11 so you’ll be able to predict that there are 11 red balls in an exceedingly bag

3. A spinner was spun 1000 times and the frequency of outcomes was recorded as in the given table.

Find (a) list the possible outcomes that you can see in the spinner (b) compare the probability of each outcome (c) find the ratio of each outcome to the total number of times that the spinner spun.

(a) T he possible outcomes are 5. They are red, orange, purple, yellow, and green. Here all the five colors occupy the same area in the spinner. They are all equally likely.

(b) Compute the probability of each event.

P (Red) = \(\frac{\text{Favorable outcomes of red}}{\text{Total number of possible outcomes}}\) = \(\frac{\text{1}}{\text{5}}\) = 0.2

Similarly, P (Orange), P (Purple), P (Yellow) and P (Green) are also \(\frac{\text{1}}{\text{5}}\) or 0.2.

(c) From the experiment the frequency was recorded in the table.

Ratio for red = \(\frac{\text{Number of outcomes of red in the above experiment}}{\text{Number of times the spinner was spun}}\) = \(\frac{\text{185}}{\text{1000}}\) = 0.185

Similarly, we can find the corresponding ratios for orange, purple, yellow, and green are 0.195, 0.210, 0.206, and 0.204 respectively. Can you see that each of the ratios is approximately equal to the probability which we have obtained in (b) [i.e. before conducting the experiment]

How do you find experimental probability?

The experimental probability of an occurrence is predicted by actual experiments and therefore the recordings of the events. It’s adequate to the amount of times an incident occurred divided by the overall number of trials.

How does one find theoretical probability?

When all possible events or outcomes are equally likely to occur, the theoretical probability is found without collecting data from an experiment.

What is experimental probability used for?

Experimental probability, also called Empirical probability, relies on actual experiments and adequate recordings of the happening of events. To work out the occurrence of any event, a series of actual experiments are conducted.

Why is experimental probability different from theoretical?

Theoretical probability describes how likely an occurrence is to occur. We all know that a coin is equally likely to land heads or tails, therefore the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently a happening actually occurred in an experiment.

Is flipping a coin theoretical or experimental probability?

So the results of flipping a coin should be somewhere around 50% heads and 50% tails since that’s the theoretical probability.

Can the experimental probability of an incident be a negative number?

No, since the quantity of trials during which the event can happen can not be negative and also the total number of trials is usually positive.

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Theoretical and experimental probability

There are two different types of probability that we often talk about: theoretical probability and experimental probability.

Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2.

Experimental probability describes how frequently an event actually occurred in an experiment. So if you tossed a coin 20 times and got heads 8 times, the experimental probability of getting heads would be 8/20, which is the same as 2/5, or 0.4, or 40%.

The theoretical probability of an event will always be the same, but the experimental probability is affected by chance, so it can be different for different experiments. The more trials you carry out (for example, the more times you toss the coin), the closer the experimental probability is likely to be to the theoretical probability.

Maybe you could try tossing a coin 20 times to see how close your experimental probability is to the theoretical probability.

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Using Theoretical and Experimental Probability to Make Predictions

Introduction.

When you are working with the probability that an event could happen, that is called theoretical probability .

For example, when rolling a typical six-sided number cube, there is only one "6" on the cube and an equal chance of any number landing face up.  

For example, if a dart is randomly thrown at a dartboard 40 times, data can be collected based on the numbered sector in which the dart lands.

Working with both theoretical and experimental probability is important, since frequently in the real world, what should happen, and what really does happen, are quite different!

Comparing Theoretical and Experimental Probabilities

In this section, you will use a spinner simulator to conduct several "spins" in order to compare theoretical probabilities with experimental probabilities.

Use the "Spinner" below which has three equal-sized sections that are blue, red, and yellow.

• Spin the spinner a total of 30 times
• Record your results in the table.

Assume that the areas of each sector of the spinner are the same.

• What is the theoretical probability of the spinner landing on each color?
• Based on the theoretical probability of the spinner landing on each color, how many spins out of 30 spins should land on each color?
• Did the actual results of the spins match the results predicted by theoretical probability? Why do you think that is the case?

Repeat the process with the same spinner for a total of 100 spins.

• Based on the theoretical probability of the spinner landing on each color, how many spins out of 100 spins should land on each color?

Using Probabilities to Make Predictions

Because theoretical and experimental probabilities are ratios, we can use proportions with probabilities to make predictions.

The results of a random survey of 8th grade students at Summit Middle School showed that 32 out of 70 students prefer listening to country music. If there are 490 students in the 8th grade at Summit Middle School, approximately how many students would be expected to prefer listening to country music?

Solve the proportion that you set up in order to determine the answer to the original question, How many students would be expected to prefer listening to country music?

1. The probability that one wristband is defective is 1 20 \frac{1}{20} . In a case of 840 wristbands, how many would be defective?

2. Benita observed that 28 out of 55 patrons at the public library used the computer. The librarian told Benita that 660 patrons enter the library throughout the day. Based on Benita's observations, how many patrons during the day would be expected to use the computer?

3. Clayton selected number tiles out of a bag. He recorded his results in the table.

Based on these results, if Clayton draws 100 tiles, how many odd numbers should he expect to draw?

You compared two different types of probability: theoretical probability and experimental probability.

Theoretical probability is the ratio of the number of favorable outcomes to the number of total possible outcomes. Experimental probability is the ratio of the number of times an event occurs to the total number of trials.

In other words, theoretical probability is a ratio that describes what should happen, but experimental probability is a ratio that describes what actually happened.

Differences between Theoretical and Experimental Probabilities You can use theoretical and experimental probabilities to distinguish between the likelihood of something happening from a purely theoretical perspective and the chances of something happening based on actual results.

Making Predictions You can also use theoretical and experimental probabilities to make predictions from situations by treating them like proportion problems.

The results of a random survey of 8th grade students at Jamison Middle School showed that 15 out of 45 students like eating lunch at 10:30 a.m. If there are 330 students in the 8th grade at Jamison Middle School, approximately how many students would be expected to prefer eating lunch at 10:30 a.m.?

110 students would like eating lunch at 10:30 a.m.

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What is the Difference Between Theoretical and Experimental Probability?

Answer: theoretical probability relies on mathematical analysis, using the ratio of favorable outcomes to possible outcomes, whereas experimental probability is derived from observed outcomes in real-world trials., what is theoretical probability.

Theoretical probability is based on mathematical analysis and relies on the assumption of equally likely outcomes in a sample space. It is calculated using the following formula:

P ( E ) = Number of Favorable Outcomes/ Total   Number   of   Possible   Outcome

• P ( E ) is the probability of event E.
• The number of favorable outcomes is determined through mathematical reasoning.

What is Experimental Probability?

Experimental probability, on the other hand, is derived from actual observations or experiments. It involves conducting trials or experiments and recording the outcomes to determine the probability. The formula for experimental probability is:

P ( E ) = ​ Number   of   Favorable   Outcomes   in   Experiment /Total Number of Trials or Experiments

• P ( E ) is the experimental probability of event E.
• The number of favorable outcomes is observed through experimentation.

Difference Between Theoretical and Experimental Probability

The following table gives the tabular difference between Theoretical and Experimental Probability:

Related Resources:

Probability Theory Experimental Probability Empirical Probability

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Percent Error / Percent Difference: Definition, Examples

Statistics Definitions >

• Percent Error
• Percent Difference

What is Percent Error?

Percent errors tells you how big your errors are when you measure something in an experiment. Smaller values mean that you are close to the accepted or real value. For example, a 1% error means that you got very close to the accepted value, while 45% means that you were quite a long way off from the true value. Measurement errors are mostly unavoidable: equipment can be imprecise, hands can shake, or your instruments just might not have the capability to measure accurately. Percent error will let you know how badly these unavoidable errors affected your results.

The formula is:

PE = (|accepted value – experimental value| \ accepted value) x 100%. Example question: The accepted distance to the moon is 238,855 miles.* You measure the distance as 249,200 miles. What is the percent error? Solution: Step 1: Insert your data into the formula: PE = (|accepted value – experimental value| \ accepted value) x 100% = ((|238,855 miles – 249,200|) \ 238,855 miles) x 100% = Step 2: Solve: (10345 \ 238,855 miles) x 100% = 0.0433 * 100% = 4.33%.

*That’s the average distance, but let’s assume it’s the distance on the day you’re taking the measurement!

Note : in some sciences, the absolute value sign is sometimes (but not always) omitted. You may want to refer to your textbook to see if the author is omitting the absolute value sign. If you aren’t sure, the most common form is with the absolute value sign.

Alternate Wording

Accepted value is sometimes called the “true” value or “theoretical” value, so you might see the formula written in slightly different ways:

• PE = (|true value – experimental value| \ true value) x 100%.
• PE = (|theoretical value – experimental value| \ theoretical value) x 100%.

All three versions of the formula mean the exact same thing — it’s just different wording.

Alternative Definition of Percent Error using Relative Error

The percentage error is sometimes reported as being 100% times the relative error . Be careful though, because there are actually two types of relative error : one for precision and one for accuracy (not sure of the difference between the two? See: Accuracy and Precision ). The definition “100% times the relative error” is only true if you are using the “accuracy” version of relative error:

• RE accuracy = (Absolute error / “True” value) * 100%.

The definition does not work if you’re using the RE for precision:

• RE precision = absolute error / measurement being taken.

What is Percent Difference?

• E 1 is the first experimental measurement.
• E 2 is the second experimental measurement.

Example question: You make two measurements in an experiment of 21 mL and 22 mL. What is the percent difference?

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Theoretical Resistance Vs Experimental

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• Start date Sep 25, 2011
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Homework Statement

Homework equations, the attempt at a solution.

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multiix said: Parallel. In this example as well since the current has to travel through extra wire which makes it a parallel. The wire's resistance adds on to the calculated resistors value. Series: The theoretical and experimental values for the resistance are different since the electricity has to travel through extra wire in case 1 and this wire causes resistance which adds to the value of the final resistance measured. The value which is more reliable for measuring the series's resistance is 58.769 Ohms as measued in Part 2 Is this correct^?

multiix said: Parallel: Rs=1/R1+1/R2

Related to Theoretical Resistance Vs Experimental

What is the difference between theoretical and experimental resistance.

Theoretical resistance refers to the predicted resistance of a material or system based on mathematical models and equations. This resistance is calculated using known physical properties and assumptions. On the other hand, experimental resistance is the actual resistance measured through physical experiments and tests.

Why is there a difference between theoretical and experimental resistance?

Theoretical resistance is based on ideal conditions and assumptions, while experimental resistance takes into account real-world variables and imperfections. Additionally, experimental resistance can be affected by external factors such as temperature, humidity, and measurement errors.

Which is more accurate: theoretical or experimental resistance?

Both theoretical and experimental resistance have their own strengths and limitations. Theoretical resistance provides a good baseline estimate, but it may not accurately reflect real-world conditions. Experimental resistance, on the other hand, is based on actual measurements and can take into account various variables, making it more accurate in some cases.

How do theoretical and experimental resistance impact scientific research?

Theoretical resistance is used to make predictions and guide research, while experimental resistance validates and refines those predictions. Both are important in the scientific process, as they work together to develop a deeper understanding of the properties and behaviors of materials and systems.

Can theoretical and experimental resistance ever be the same?

In ideal conditions, theoretical and experimental resistance can be the same. However, in most cases, there will be some discrepancy due to the limitations and assumptions of theoretical models and the complexity of real-world systems. Scientists strive to minimize this difference through further research and refinement of theoretical models.

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What is meant by experimental value?

In science, and most specifically chemistry, the accepted value denotes a value of a substance accepted by almost all scientists and the experimental value denotes the value of a substance’s properties found in a localized lab.

Table of Contents

What are experimental values in physics?

Experimental value consists of the measurements taken during an experimental run. When taking experiment measurements, the goal is to arrive at a value that is accurate and precise.

How do you find the experimental value in physics?

What is experimental value and theoretical value?

The experimental value is your calculated value, and the theoretical value is your known value. A percentage very close to zero means you are very close to your targeted value, which is good.

Why are theoretical and experimental values different?

This difference is due to three factors: the variation of the diffusion voltage, the nonzero electric field at the boundaries of the depletion region, and the contribution of electrons and holes. The exact values also disagree with the experimental results.

What is true value physics?

The actual population value that would be obtained with perfect measuring instruments and without committing any error of any type, both in collecting the primary data and in carrying out mathematical operations.

What is the difference between theoretical and experimental?

The difference between theoretical and experimental probability is that theoretical is based on knowledge and mathematics. Experimental probability is based on trials or experiments. Theoretical probability is what should happen. Experimental probability is what does happen.

What is the difference between experimental and theoretical physics?

Theoretical physicists devise mathematical models to explain the complex interactions between matter and energy, while experimental physicists conduct tests on specific physical phenomena, using advanced tools from lasers to particle accelerators and telescopes, to arrive at answers.

What is theoretical and experimental?

Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently an event actually occurred in an experiment.

What is the difference between the experimental value of a measurement and the accepted value?

The accepted value of a measurement is the true or correct value based on general agreement with a reliable reference. For aluminum, the accepted density is 2.70g/cm3. The experimental value of a measurement is the value that is measured during the experiment.

What is the experimental value in percent error?

Percent error is the difference between a measured or experiment value and an accepted or known value, divided by the known value, multiplied by 100%. For many applications, percent error is always expressed as a positive value. The absolute value of the error is divided by an accepted value and given as a percent.

How do you compare two experimental values?

If the experimental value may be greater or less than the true value, use a two sided t-score. If specifically testing for a significant increase or decrease (but not both) use a single sided value for tc. Comparing two experimental averages. The t-test may also be used to compare two experimental averages.

What is a theoretical value?

Sometimes referred to as a fair or hypothetical value, a theoretical value is the estimated price of an option. Sometimes referred to as a fair or hypothetical value, a theoretical value is the estimated price of an option. The options pricing may have to do with buying, selling, or a combination of the two.

How do you find theoretical value?

This value is calculated by determining the difference between the subscription price the investor paid and the theoretical ex-right price. Considering the example used above, the calculation for a theoretical nil paid price looks like this: $40 – $38 = $2.

How do you find experimental value in R?

Rearrange PV = nRT to solve for R. Plug your experimental numbers in and solve for experimental value of R. Remember that P must be in ATM, V must be in L, and T must be in K.

Why might your experimental value vary from the expected value?

Some factors that contribute to experimental values being different from actual values are human errors, procedural errors, and environmental errors. These can be random errors or systematic errors . Instrumental errors are due to the inaccuracy of the instrument. Systematic errors can be eliminated.

How do you compare theoretical and experimental probability?

Theoretical probability is what we expect to happen, where experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes.

What is the difference between theoretical and experimental sometimes called empirical probability?

In conclusion, theoretical probability is based on the assumption that outcomes have an equal chance of occurring while empirical probability is based on the observations of an experiment. There are two other types of probabilities and these are axiomatic probability and subjective probability.

What is the difference between observed value and true value?

Answer: The difference between the true value and the measured value of a physical quantity is called the error in its measurement.

What is place value and true value?

Place value is the value represented by a digit in a number according to its position in the number. Face value is the actual value of a digit in a number. To get the place value of a number, we multiply the digit value with its numerical value.

What is the meaning of actual value?

Definition. Actual value is the customer’s current and future value if the current level of business is maintained over time. This dimension of value includes revenue, but also elements such as how engaged the customer is in the business, communications, and referrals.[1]

What is a experimental method in physics?

Experimental physics uses two main methods of experimental research, controlled experiments, and natural experiments. Controlled experiments are often used in laboratories as laboratories can offer a controlled environment.

Why is experimental theory necessary?

Experiment can provide hints toward the structure or mathematical form of a theory and it can provide evidence for the existence of the entities involved in our theories. Finally, it may also have a life of its own, independent of theory.

What is an example of theoretical and experimental probability?

For example, if a dice is rolled 6000 times and the number ‘5’ occurs 990 times, then the experimental probability that ‘5’ shows up on the dice is 990/6000 = 0.165. For example, the theoretical probability that the number ‘5’ shows up on a dice when rolled is 1/6 = 0.167.

Who is the father of experimental physics?

Galileo Galilei was and is sometimes referred to as “the father of experimental science.” Galileo didn’t take much on faith, rather, he tested his ideas through experiments and expressed them in mathematical form. Hence, option C is the correct answer.

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What is the difference between Accepted Value vs. Experimental Value?

#"Error" = "|experimental value - accepted value|"#

The difference is usually expressed as percent error .

#"% error" = "|experimental value - accepted value|"/"experimental value" × 100 %#

For example, suppose that you did an experiment to determine the boiling point of water and got a value of 99.3 °C.

Your experimental value is 99.3 °C.

The theoretical value is 100.0 °C.

The experimental error is #"|99.3 °C - 100.0 °C| = 0.7 °C"#

The percent error is #"|99.3 °C - 100.0 °C|"/"100.0 °C" = "0.7 °C"/"100.0 °C" × 100% = 0.7 %#

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Comparing Lattice Enthalpies ( AQA A Level Chemistry )

Revision note.

Chemistry Lead

Comparing Lattice Enthalpies

How accurate are lattice enthalpies.

• the geometry of the ionic solid
• the charge on the ions
• the distance between the ions
• This has been calculated for a number of ionic solids and allows a comparison between theoretical lattice enthalpies and experimental lattice enthalpies obtained from Born-Haber cycles

Table comparing theoretical and experimental lattice enthalpies

• You can see from the table that there is quite close agreement between the two values for the lattice enthalpy of sodium chloride
• The calculation of the theoretical value is based on an assumption that the substance is a highly ionic compound with only electrostatic attraction between cations and anions

The ionic model for sodium chloride

• However, the difference between theoretical and experimental lattice enthalpy increases for zinc sulfide
• This suggests that the bonding is not purely ionic and some covalent character is present
• Zinc is a smaller ion with a greater charge (+2) than sodium(+1)
• Zinc ions attract electron density towards themselves, distorting the electron cloud and making the bonding slightly covalent
• Sulfide ions are larger ions than chloride ions(-1) with a greater negative charge (-2)
• The electron cloud around sulfide ions is more easily distorted than in chloride ions leading to further covalent character

• As you move left to right across the period table the lattices become less ionic and more covalent l eading to a discrepancy in the lattice enthalpy values
• The result of these analyses provides strong evidence that supports the ionic model for some compounds like sodium chloride

The distortion of the electron clouds is known as polarisation and illustrates that bonding is not either pure ionic or covalent, but rather a continuum between the two extremes.

Factors affecting lattice enthalpy

• The two key factors which affect lattice energy, Δ H latt ꝋ , are the charge and radius of the ions that make up the crystalline lattice

Ionic radius

• The lattice energy becomes less exothermic as the ionic radius of the ions increases
• This is because the charge on the ions is more spread out over the ion when the ions are larger
• The attraction between ions is between the centres of the ions involved, so the bigger the ions the bigger the distance between the centre of the ions
• Therefore, the electrostatic forces of attraction between the oppositely charged ions in the lattice are weaker
• Since both compounds contain a fluoride (F - ) ion, the difference in lattice energy must be due to the caesium (Cs + ) ion in CsF and potassium (K + ) ion in KF
• Potassium is a Group 1 and Period 4 element
• Caesium is a Group 1 and Period 6 element
• This means that the Cs + ion is larger than the K + ion
• There are weaker electrostatic forces of attraction between the Cs + and F - ions compared to K + and F - ions
• As a result, the lattice energy of CsF is less exothermic than that of KF

The lattice energies get less exothermic as the ionic radius of the ions increases

Ionic charge

• The lattice energy gets more exothermic as the ionic charge of the ions increases
• The greater the ionic charge, the higher the charge density
• This results in stronger electrostatic attraction between the oppositely charged ions in the lattice
• As a result, the lattice energy is more exothermic
• Calcium oxide is an ionic compound which consists of calcium (Ca 2+ ) and oxide (O 2- ) ions
• Potassium chloride is formed from potassium (K + ) and chloride (C l - ) ions
• The ions in calcium oxide have a greater ionic charge than the ions in potassium chloride
• This means that the electrostatic forces of attraction are stronger between the Ca 2+ and O 2- compared to the forces between K + and C l -
• Therefore, the lattice energy of calcium oxide is more exothermic, as more energy is released upon its formation from its gaseous ions
• Ca 2+ and O 2- are also smaller ions than K + and C l - , so this also adds to the value for the lattice energy being more exothermic

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