Sample Variance

#595 / Prob & Stats Easy

Calculate the sample variance for the values: 1, 2, 3, 10, 4.

Expand Hint

Sample variance:

$$$s^2=\frac{1}{(n-1)}\sum_{i=1}^{n}(X_i-\mu)^2$$$

where $$n$$ is the sample size, $$\mu$$ is the arithmetic mean of the sampled items, and $$X_i$$ is the value of the individual observation.

Hint 2

To find the mean:

$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}$$$

First, let’s find the mean of the values:

$$$\mu=\frac{sum\:of\:terms}{number\:of\:terms}=\frac{1+2+3+10+4}{5}=\frac{20}{5}=4$$$

Sample variance:

$$$s^2=\frac{1}{(n-1)}\sum_{i=1}^{n}(X_i-\mu)^2$$$

where $$n$$ is the sample size, $$\mu$$ is the arithmetic mean of the sampled items, and $$X_i$$ is the value of the individual observation.

$$$s^2=\frac{(1-4)^2+(2-4)^2+(3-4)^2+(10-4)^2+(4-4)^2}{(5-1)}$$$

$$$=\frac{(-3)^2+(-2)^2+(-1)^2+(6)^2+(0)^2}{4}$$$

$$$=\frac{9+4+1+36+0}{4}=\frac{50}{4}=12.5$$$

12.5

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