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In the data set below, what is the variance? $\newline$ $1, 9, 1, 1, 8, 4$ $\newline$ 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

1, 9, 1, 1, 8, 4

\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. $\newline$ $(1 - 4)^2 + (9 - 4)^2 + (1 - 4)^2 + (1 - 4)^2 + (8 - 4)^2 + (4 - 4)^2$ $\newline$ $= (-3)^2 + (5)^2 + (-3)^2 + (-3)^2 + (4)^2 + (0)^2$ $\newline$ $= 9 + 25 + 9 + 9 + 16 + 0$ $\newline$ $= 68$
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 $\sigma^2$ = $\frac{68}{6}$ $\newline$ Variance $\sigma^2$ = $11$ . $333$ ... $\newline$ Rounded to the nearest tenth, Variance $\sigma^2$ $\approx 11.3$

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