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In the data set below, what is the variance? $\newline$ $8, 1, 5, 3, 9$ $\newline$ 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

8, 1, 5, 3, 9

\newline

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

\newline

variance

(\sigma^2)

: _____

Subtract and Square: Now, subtract the mean from each data point and square the result. $\newline$ $(8 - 5.2)^2 = (2.8)^2 = 7.84$ $\newline$ $(1 - 5.2)^2 = (-4.2)^2 = 17.64$ $\newline$ $(5 - 5.2)^2 = (-0.2)^2 = 0.04$ $\newline$ $(3 - 5.2)^2 = (-2.2)^2 = 4.84$ $\newline$ $(9 - 5.2)^2 = (3.8)^2 = 14.44$
Add Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $7.84 + 17.64 + 0.04 + 4.84 + 14.44$ $\newline$ Sum of squared differences = $44.8$
Calculate Variance: Divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{44.8}{5}$ $\newline$ Variance $\sigma^2$ = $8.96$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 9.0$

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