Sample Variance
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
Time Analysis
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