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In the data set below, what is the variance? $\newline$ $8, 3, 3, 8, 1, 7$ $\newline$ 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, 3, 3, 8, 1, 7

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $(8 - 5)^2 + (3 - 5)^2 + (3 - 5)^2 + (8 - 5)^2 + (1 - 5)^2 + (7 - 5)^2$ $\newline$ $= 3^2 + (-2)^2 + (-2)^2 + 3^2 + (-4)^2 + 2^2$ $\newline$ $= 9 + 4 + 4 + 9 + 16 + 4$ $\newline$ $= 46$
Find Variance: Finally, we divide the sum of squared differences by the number of values to find the variance. $\newline$ Variance $\sigma^2$ = Sum of squared differences / Number of values $\newline$ Variance $\sigma^2$ = $\frac{46}{6}$ $\newline$ Variance $\sigma^2$ = $7$ . $666$ ... $\newline$ Rounded to the nearest tenth: $7.7$

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