What are the variance and standard deviation of {1, 1, 1, 1, 1, 80, 1, 1, 1, 1, 1, 1}?

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What are the variance and standard deviation of {1, 1, 1, 1, 1, 80, 1, 1, 1, 1, 1, 1}?

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Answer 1 · 2016-07-14T18:11:53

The population variance is:

$sigma^2 ~= 476.7$

and the populations standard deviation is the square root of this value:

$sigma ~= 21.83$

Explanation:

First, let's assume that this is the entire population of values. Therefore we are looking for the population variance . If these numbers were a set of samples from a larger population, we would be looking for the **sample variance ** which differs from the population variance by a factor of $n//(n-1)$

The formula for the population variance is

$sigma^2=1/N sum_(i=1)^N(x_i-mu)^2$

where $mu$ is the population mean, which can be calculated from

$mu = 1/N sum_(i=1)^N x_i$

In our population the mean is

$mu = (1+1+1+1+1+80+1+1+1+1+1+1)/12=91/12=7.58bar3$

Now we can proceed with the variance calculation:

$sigma^2=(11*(1-7.58bar3)^2+ (80-7.58bar3)^2)/12$

$sigma^2 ~= 476.7$

and the standard deviation is the square root of this value:

$sigma ~= 21.83$

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What are the variance and standard deviation of {1, 1, 1, 1, 1, 80, 1, 1, 1, 1, 1, 1}?

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