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

Macy Villanueva

Macy Villanueva

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2022-08-19

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

Answer & Explanation

uglasiteveh

uglasiteveh

Beginner2022-08-20Added 6 answers

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
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 = 1 + 1 + 1 + 1 + 1 + 80 + 1 + 1 + 1 + 1 + 1 + 1 12 = 91 12 = 7.58 3 ¯
Now we can proceed with the variance calculation:
σ 2 = 11 ( 1 7.58 3 ¯ ) 2 + ( 80 7.58 3 ¯ ) 2 12
σ 2 476.7
and the standard deviation is the square root of this value:
σ 21.83

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