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In the data set below, what is the variance? $\newline$ $3, 3, 9, 1, 6$ $\newline$ 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

3, 3, 9, 1, 6

\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. $\newline$ $(3 - 4.4)^2 = (-1.4)^2 = 1.96$ $\newline$ $(3 - 4.4)^2 = (-1.4)^2 = 1.96$ $\newline$ $(9 - 4.4)^2 = (4.6)^2 = 21.16$ $\newline$ $(1 - 4.4)^2 = (-3.4)^2 = 11.56$ $\newline$ $(6 - 4.4)^2 = (1.6)^2 = 2.56$
Add Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $1.96 + 1.96 + 21.16 + 11.56 + 2.56$ $\newline$ Sum of squared differences = $39.2$
Calculate Variance: Divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{39.2}{5}$ $\newline$ Variance $\sigma^2$ = $7.84$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 7.8$

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