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In the data set below, what is the variance? $\newline$ $8, 7, 1, 9, 2, 6$ $\newline$ 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

8, 7, 1, 9, 2, 6

\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. $\newline$ $(8 - 5.5)^2 + (7 - 5.5)^2 + (1 - 5.5)^2 + (9 - 5.5)^2 + (2 - 5.5)^2 + (6 - 5.5)^2$ $\newline$ = $(2.5)^2 + (1.5)^2 + (-4.5)^2 + (3.5)^2 + (-3.5)^2 + (0.5)^2$ $\newline$ = $6.25 + 2.25 + 20.25 + 12.25 + 12.25 + 0.25$ $\newline$ = $53.5$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = Sum of squared differences / Number of data points $\newline$ Variance $\sigma^2$ = $\frac{53.5}{6}$ $\newline$ Variance $\sigma^2$ = $8$ . $916666$ ... $\newline$ Rounded to the nearest tenth: $8.9$

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