What is the variance of {-13, 10, 8, -3, 6, 12, 7}?

Question

Adrian Alexander · Accepted Answer

Depending upon whether the given data is to be taken as the entire population (all values) or a sample from some larger population:
Population variance #sigma^2 ~= 66.7#
Sample variance #s^2 ~=77.8#

This can be determined using standard built-in functions of a scientific calculator or a spread sheet (as below):

Audrey Andrews · Answer

undefined To calculate the variance of a set of numbers, we first need to find the mean (average) of the numbers. Then, we calculate the squared difference between each number and the mean, sum up these squared differences, and divide by the total number of observations.

First, find the mean:
Mean = (-13 + 10 + 8 - 3 + 6 + 12 + 7) / 7
Mean = 27 / 7
Mean = 3.857 (rounded to three decimal places)

Now, calculate the squared differences for each number:
(-13 - 3.857)^2 = 272.265
(10 - 3.857)^2 = 38.729
(8 - 3.857)^2 = 16.765
(-3 - 3.857)^2 = 52.561
(6 - 3.857)^2 = 4.665
(12 - 3.857)^2 = 65.961
(7 - 3.857)^2 = 9.361

Next, sum up these squared differences:
272.265 + 38.729 + 16.765 + 52.561 + 4.665 + 65.961 + 9.361 = 460.307

Finally, divide the sum by the total number of observations (7 in this case) to get the variance:
Variance = 460.307 / 7 ≈ 65.757 (rounded to three decimal places)

So, the variance of the set {-13, 10, 8, -3, 6, 12, 7} is approximately 65.757.