What is the variance of {-4, 5, 8 ,-1, 0 ,4 ,-12, 4}?

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Quinn Alvarez · Accepted Answer

First, let&#039;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      σ          2        =      1    N        ∑          i      =      1              N        (      x          i        −  μ      )          2      where   μ is the population mean, which can be calculated from  μ  =      1    N        ∑          i      =      1              N            x          i      In our population the mean is  μ  =            −      4      +      5      +      8      −      1      +      0      +      4      −      12      +      4        8    =      4    8    =      1    2  Now we can proceed with the variance calculation:      σ          2                  (      −      4      −              1        2                    )                  2                    +      (      5      −              1        2                    )                  2                    +      (      8      −              1        2                    )                  2                    +      (      −      1      −              1        2                    )                  2                    +      (      0      −              1        2                    )                  2                    +      (      4      −              1        2                    )                  2                    +      (      −      12      −              1        2                    )                  2                    +      (      4      −              1        2                    )                  2                      8        σ          2        =  35

What is the variance of {-4, 5, 8 ,-1, 0 ,4 ,-12, 4}?

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