How To Calculate Percent Error Statistics
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Percent Error Definition
in lab experiments, specifically percent error. Of all of the terms below, you are probably most familiar with "arithmetic mean", otherwise known as an "average". Mean -- add all of the values and divide by the total number of data points Error -- subtract the theoretical value (usually the number the professor has as the target value) from your experimental data point. Percent error -- take the absolute value of the error divided by the theoretical value, then multiply by 100. Deviation -- subtract the mean from the experimental data point Percent deviation -- divide the deviation by the mean, then multiply by 100: Arithmetic mean = ∑ data pointsnumber of data points (n) Error = Experimental value - "true" or theoretical value Percent Error = Error Theoretical value ∗100 Deviation = Experimental value - arithmetic mean Percent Deviation = DeviationTheoretical value ∗100 A sample problem should make this all clear: in the lab, the boiling point of a liquid, which has a theoretical value of 54.0° C, was measured by
a percentage of one (or both) values Use Percentage Change when comparing an Old Value to a New Value Use Percentage Error when comparing an Approximate Value to an Exact Value Use Percentage Difference when both
Percent Deviation Formula
values mean the same kind of thing (one value is not obviously older what is a good percent error or better than the other). (Refer to those links for more details) How to Calculate Step 1: Subtract one value from percent error worksheet the other Step 2: Then divide by ... what? Percentage Change: Divide by the Old Value Percentage Error: Divide by the Exact Value Percentage Difference: Divide by the Average of The Two Values Step 3: https://www.shodor.org/unchem-old/math/stats/index.html Is the answer negative? Percentage Change: a positive value is an increase, a negative value is a decrease. Percentage Error: ignore a minus sign (just leave it off), unless you want to know if the error is under or over the exact value Percentage Difference: ignore a minus sign, because neither value is more important, so being "above" or "below" does not make sense. Step 4: Convert this into a http://www.mathsisfun.com/data/percentage-difference-vs-error.html percentage (multiply by 100 and add a % sign) The Formulas (Note: the "|" symbols mean absolute value, so negatives become positive.) Percent Change = New Value - Old Value × 100% |Old Value| Example: There were 200 customers yesterday, and 240 today: 240 - 200 × 100% = (40/200) × 100% = 20% |200| A 20% increase. Percent Error = |Approximate Value - Exact Value| × 100% |Exact Value| Example: I thought 70 people would turn up to the concert, but in fact 80 did! |70 - 80| × 100% = (10/80) × 100% = 12.5% |80| I was in error by 12.5% (Without using the absolute value, the error is -12.5%, meaning I under-estimated the value) Percentage Difference = | First Value - Second Value | × 100% (First Value + Second Value)/2 Example: "Best Shoes" gets 200 customers, and "Cheap Shoes" gets 240 customers: | 240 - 200 | × 100% = |40/220| × 100% = 18.18...% (200+240)/2 Percentage Difference Percentage Error Percentage Change Percentage Index Search :: Index :: About :: Contact :: Contribute :: Cite This Page :: Privacy Copyright © 2014 MathsIsFun.com
or real value. Then, convert the ratio to a percent. We can expresss the percent error with the following formula shown below: The amount of error is a http://www.basic-mathematics.com/calculating-percent-error.html subtraction between the measured value and the accepted value Keep in mind that when computing the amount of error, you are always looking for a positive value. Therefore, always subtract the smaller value http://www.forecastpro.com/Trends/forecasting101August2011.html from the bigger. In other words, amount of error = bigger − smaller Percent error word problem #1 A student made a mistake when measuring the volume of a big container. He found percent error the volume to be 65 liters. However, the real value for the volume is 50 liters. What is the percent error? Percent error = (amount of error)/accepted value amount of error = 65 - 50 = 15 The accepted value is obviously the real value for the volume, which 50 So, percent error = 15/50 Just convert 15/50 to a percent. We can do this multiplying how to calculate both the numerator and the denominator by 2 We get (15 × 2)/(50 × 2) = 30/100 = 30% Notice that in the problem above, if the true value was 65 and the measured value was 50, you will still do 65 − 50 to get the amount of error, so your answer is still positive as already stated However, be careful! The accepted value is 65, so your percent error is 15/65 = 0.2307 = 0.2307/1 = (0.2307 × 100)/(1 × 100) = 23.07/100 = 23.07% Percent error word problem #2 A man measured his height and found 6 feet. However, after he carefully measured his height a second time, he found his real height to be 5 feet. What is the percent error the man made the first time he measured his height? Percent error = (amount of error)/accepted value amount of error = 6 - 5 = 1 The accepted value is the man's real height or the value he found after he carefully measured his height, or 5 So, percent error = 1/5 Just convert 1/5 to a percent. We can do this multiplying both the numerator and the denominator by 2
Interpretation of these statistics can be tricky, particularly when working with low-volume data or when trying to assess accuracy across multiple items (e.g., SKUs, locations, customers, etc.). This installment of Forecasting 101 surveys common error measurement statistics, examines the pros and cons of each and discusses their suitability under a variety of circumstances. The MAPE The MAPE (Mean Absolute Percent Error) measures the size of the error in percentage terms. It is calculated as the average of the unsigned percentage error, as shown in the example below: Many organizations focus primarily on the MAPE when assessing forecast accuracy. Most people are comfortable thinking in percentage terms, making the MAPE easy to interpret. It can also convey information when you don’t know the item’s demand volume. For example, telling your manager, "we were off by less than 4%" is more meaningful than saying "we were off by 3,000 cases," if your manager doesn’t know an item’s typical demand volume. The MAPE is scale sensitive and should not be used when working with low-volume data. Notice that because "Actual" is in the denominator of the equation, the MAPE is undefined when Actual demand is zero. Furthermore, when the Actual value is not zero, but quite small, the MAPE will often take on extreme values. This scale sensitivity renders the MAPE close to worthless as an error measure for low-volume data. The MAD The MAD (Mean Absolute Deviation) measures the size of the error in units. It is calculated as the average of the unsigned errors, as shown in the example below: The MAD is a good statistic to use when analyzing the error for a single item. However, if you aggregate MADs over multiple items you need to be careful about high-volume products dominating the results--more on this later. Less Common Error Measurement Statistics The MAPE and the MAD are by far the most commonly used error measurement statistics. There are a slew of alternative statistics in the forecasting literature, many of which are variations on the MAPE and the MAD. A few of the more important ones are listed below: MAD/Mean Ratio. The MAD/Mean ratio is an alternative to the MAPE that is better suited to intermittent and low-volume data. As stated previously, percentage errors cannot be calculated when the actual equals zero and can take on extrem