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This article was co-written by Jake Adams. Jake Adams is a tutor and owner of PCH Tutors, a business in Malibu, California that provides tutoring and learning resources for kindergarten through college, SAT & ACT preparation materials, and private tutoring. college admissions inquiries. With over 11 years of experience as a tutor, Jake is also the CEO of Simplifi EDU – an online tutoring service with the goal of helping customers access a network of excellent tutors in California. Jake holds a bachelor’s degree in international business and marketing from Pepperdine University.
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In terms of formulas, the percentage error is calculated as the magnitude of the difference between the exact value and the estimated value divided by the exact value, multiplied by 100 (expressed as a %). It basically shows you the difference between the estimated value and the correct value. There are two possible scenarios for errors: measurement errors (either by tools or people) and approximations (such as when rounding). In any case, the formula for calculating the percentage of error is very simple and easy to follow.
Steps
Substitute the values into the formula
- The estimated value is the relative value, and the exact value is the actual value (or accepted theoretical value).
- For example, if you guess there are 9 oranges in the bag, but there are actually 10, then 9 is the estimated value and 10 is the correct value.
- This difference is the magnitude of the difference between the estimated value and the actual value. This value tells us how much the actual result differs from the estimate.
- In the number of oranges example, we have: 9 – 10 = -1. Absolute value of -1 or |-1| = 1.
- If the difference is positive, keep the result. Example: 12 apples (estimated) – 10 apples (real) = 2. The absolute value of (|2|) is 2.
- In statistics, when referring to the absolute value, you do not need to care about the direction in which the guess is deviated from reality, such as being too high (positive number) or too low (negative number). You just need to know HOW MUCH difference you have estimated from the correct value.
- We have: 1/|10| = 1/10.
- In some cases, the exact value may be negative. Then you just get the absolute value of the exact value by omitting the negative sign. [5] X Research Sources
Return as a percentage to complete the answer
- If you don’t have a calculator, you’ll have to do long division to convert the fraction to a decimal. Usually, we just need to round from 4 to 5 digits after the comma is enough.
- Always divide a positive number by a positive number when converting from fractions to decimals.
- In this example, we have: 0.1 x 100 = 10. So, the percentage error in estimating the number of oranges is 10%.
- In the above example, to check if the estimated number of oranges is 10% different from the actual number of oranges, calculate 10% of 10 oranges. If the result is 1, you have the correct answer. We have: 10 x 10% = 10 x 0.1 = 1.
- 9 balls + 1 = 10 balls. So the 9 oranges on the estimate are 1 wrong, or in other words, 10% compared to the actual 10 oranges.
Advice
- The estimated value is also known as the estimated value, the measured value or the empirical value. The exact value is also known as the actual value or the accepted theoretical value.
- Fun fact: since we take the absolute value of the difference between the estimated value and the exact value, the order in which this subtraction is performed does not matter. Example: |8 – 4| = 4 and |4 – 8| = |-4| = 4. The result is the same!
This article was co-written by Jake Adams. Jake Adams is a tutor and owner of PCH Tutors, a business in Malibu, California that provides tutoring and learning resources for kindergarten through college, SAT & ACT preparation materials, and private tutoring. college admissions inquiries. With over 11 years of experience as a tutor, Jake is also the CEO of Simplifi EDU – an online tutoring service with the goal of helping customers access a network of excellent tutors in California. Jake holds a bachelor’s degree in international business and marketing from Pepperdine University.
This article has been viewed 6,440 times.
In terms of formulas, the percentage error is calculated as the magnitude of the difference between the exact value and the estimated value divided by the exact value, multiplied by 100 (expressed as a %). It basically shows you the difference between the estimated value and the correct value. There are two possible scenarios for errors: measurement errors (either by tools or people) and approximations (such as when rounding). In any case, the formula for calculating the percentage of error is very simple and easy to follow.
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