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In the data set below, what is the variance? $\newline$ $5, 8, 8, 6, 1$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Variance and standard deviation

Full solution

Q. In the data set below, what is the variance?

\newline

5, 8, 8, 6, 1

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

variance

(\sigma^2)

: _____

Calculate squared differences: Now, calculate the squared differences from the mean for each data point. $\newline$ $(5 - 5.6)^2 + (8 - 5.6)^2 + (8 - 5.6)^2 + (6 - 5.6)^2 + (1 - 5.6)^2$ $\newline$ = $(-0.6)^2 + (2.4)^2 + (2.4)^2 + (0.4)^2 + (-4.6)^2$ $\newline$ = $0.36 + 5.76 + 5.76 + 0.16 + 21.16$ $\newline$ = $33.2$
Find the variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{33.2}{5}$ $\newline$ Variance $\sigma^2$ = $6.64$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 6.6$

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