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What is the Coefficient the Variation?

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The coefficient of sports (CV) is a measure up of loved one variability. It is the ratio of the standard deviation come the median (average). For example, the expression “The traditional deviation is 15% of the mean” is a CV.

The CV is particularly useful once you desire to compare outcomes from two different surveys or tests the have different measures or values. For example, if you are comparing the outcomes from two tests that have various scoring mechanisms. If sample A has actually a CV of 12% and also sample B has a CV that 25%, you would certainly say the sample B has more variation, relative to the mean.

Formula

The formula because that the coefficient of variation is:

Coefficient of variation = (Standard Deviation / Mean) * 100.In symbols: CV = (SD/x̄) * 100.

Multiplying the coefficient by 100 is one optional step to acquire a percentage, together opposed come a decimal.

Coefficient of sport Example

A researcher is comparing 2 multiple-choice exam with different conditions. In the an initial test, a usual multiple-choice check is administered. In the 2nd test, alternative choices (i.e. Incorrect answers) room randomly assigned to test takers. The outcomes from the two tests are:

Regular TestRandomized Answers
Mean59.944.8
SD10.212.7

Trying to to compare the 2 test outcomes is challenging. Comparing typical deviations doesn’t really work, because the means are additionally different. Calculation using the formula CV=(SD/Mean)*100 helps to make sense of the data:

Regular TestRandomized Answers
Mean59.944.8
SD10.212.7
CV17.0328.35

Looking at the traditional deviations that 10.2 and 12.7, you might think the the test have comparable results. However, as soon as you change for the distinction in the means, the outcomes have much more significance:Regular test: CV = 17.03Randomized answers: CV = 28.35

The coefficient of sports can also be supplied to compare variability between different measures. For example, you can compare IQ scores come scores ~ above the Woodcock-Johnson III tests of Cognitive Abilities.

Note: The Coefficient of Variation should only be supplied to compare positive data on a ratio scale. The CV has tiny or no an interpretation for dimensions on one interval scale. Instances of expression scales include temperatures in Celsius or Fahrenheit, if the Kelvin range is a proportion scale the starts at zero and cannot, through definition, take on a an adverse value (0 degrees Kelvin is the lack of heat).

How to discover a Coefficient that Variation: Overview.

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Use the following formula to calculate the CV by hand because that a populace or a sample.

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These formulas because that coefficient that variation offer percentages. To gain a decimal, omit multiplying by 100.


σ is the conventional deviation for a population, i m sorry is the exact same as “s” for the sample.μ is the mean for the population, which is the exact same as XBar in the sample.


In other words, to uncover the coefficient of variation, division the traditional deviation through the mean and also multiply by 100.

How to uncover a coefficient of sports in Excel.

You deserve to calculate the coefficient of sport in Excel making use of the formulas for standard deviation and mean. Because that a provided column of data (i.e. A1:A10), you might enter: “=stdev(A1:A10)/average(A1:A10)) then multiply by 100.

How to uncover a Coefficient of sports by hand: Steps.

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Example question: two versions that a check are offered to students. One test has pre-set answers and also a 2nd test has actually randomized answers. Uncover the coefficient of variation.

Regular TestRandomized Answers
Mean50.145.8
SD11.212.9

Step 1: Divide the typical deviation by the average for the very first sample:11.2 / 50.1 = 0.22355

Step 2: Multiply action 1 through 100:0.22355 * 100 = 22.355%

Step 3: Divide the standard deviation by the median for the 2nd sample:12.9 / 45.8 = 0.28166