How Do You Find the Standard Deviation?


Quick Answer

To calculate standard deviation, calculate the mean of the sample numbers by adding them up and dividing by the number of terms. Subtract the mean from each number and square the result. Add up these numbers and divide by the number of terms for the variance. The square root of this is the standard deviation.

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Full Answer

Consider a case in which five students take a test. The material was apparently quite difficult because the five grades were 60, 47, 30, 43 and 17, and the principal wants to know the statistical measures for these students. Add up the five numbers and divide by five for the mean: 39.4.

Each student's difference from the mean is 20.6, 7.6, 3.6, -9.4 and -22.4. Square each of these numbers and add them together to get a sum of 1,085.2. Divide this by five (the number of the terms) to get 217. This is the variance, so take the square root of this to get the standard deviation, which is 14.73. This means that any tests more than 14.73 away from 39.4 are outside one standard deviation from the mean.

Three of the numbers are within the range, while 60 and 17 are not. This wide range calls the results into question, but the sample size is fairly small.

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