How to calculate variance of 3 5 6 4 7 7 8?

Answer 1

To calculate variance, (population standard deviation squared), usually written as σ2, first find the mean.

In this case, ( 3 + 5 + 6 + 4 + 7 + 7 +8 ) / 7 = 40/7 ≈ 5.7143

Then find the difference between every number and the mean.

5.7143 - 3 = 2.7143

5.7143 - 5 = 0.7143

5.7143 - 6 = -0.2857

5.7143 - 4 = 1.7143

5.7143 - 7 = -1.2857

5.7143 - 7 = -1.2857

5.7143 - 8 = -2.2857

Then square all of the differences.

7.3674

0.5102

0.0816

2.9388

1.6530

1.6530

5.2244

Then add the products together.

19.4284

Then divide by the number of numbers in the set of data (7) for the variance.

σ2 ≈ 2.78

Since you are using the entire population, you use the population standard deviation instead of the sample standard deviation.

In statistics, you are more likely to see sample standard deviation, but since there are only seven numbers in the data set, we use the population standard deviation.