How to Calculate Sample Variance of a Population

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The variance is a measure of the spread of a set of numbers. For example, the set 2, 3, 2, 3, 2, 3 and the set 1, 4, 1, 4, 0, 5 both have the same mean (2.5), but the former is more closely bound around 2.5.


The sample variance is the variance of a sample of a population. For example, you might want the variance of the weight of adult American men. But you can't weigh every man in America, so you take a sample and compute the variance of that sample.

Things You'll Need

  • Calculator
  • Take a sample of the population. One way to take a random sample is to write down the name of each person (or subject) in your population, number them sequentially and then use a random number table to pick a sample.

    The larger your sample, the more accurate your estimate of the variance will be, but the higher the costs in time and money of obtaining your sample.

  • Find the mean of the sample. The mean is the total of all the values in the sample divided by the number of subjects in the sample. For example, if you take a sample of five people and get weights of 130, 140, 150, 160 and 170, the mean is (130 + 140 + 150 + 160 + 170)/5 = 150.

  • Subtract each value from the mean. In the example: 130 - 150 = -20, 140 - 150 = -10, 150 - 150 = 0, 160 - 150 = 10 and 170 - 150 = 20.

  • Square each of the values from Step 3. In the example -20^2 = 400, -10^2 = 100, 0^2 = 0, 10^2 = 100 and 20^2 = 400.

  • Add up the results from Step 4. In the example 400 + 100 + 0 + 100 + 400 = 1,000.

  • Divide the result in Step 5 by the number of subjects. This is the sample variance. In the example, 1,000/5 = 200.

Tips & Warnings

  • If you want to estimate the variance of the population, in the last step, divide by n - 1 instead of n.

References

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