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In the data set below, what is the variance? $\newline$ $6, 7, 1, 3, 9$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Variance and standard deviation

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Q. In the data set below, what is the variance?

\newline

6, 7, 1, 3, 9

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Variance: Now, let's do the variance thing. $\newline$ We need to sum up each $(\text{number} - \text{mean})^2$ . $\newline$ So, $(6 - 5.2)^2 + (7 - 5.2)^2 + (1 - 5.2)^2 + (3 - 5.2)^2 + (9 - 5.2)^2$ $\newline$ That's $(0.8)^2 + (1.8)^2 + (-4.2)^2 + (-2.2)^2 + (3.8)^2$ $\newline$ Which is $0.64 + 3.24 + 17.64 + 4.84 + 14.44$ $\newline$ All that adds up to $40.8$
Sum of Squares: Last step, we divide by the number of data points to get the variance. $\newline$ Variance = $\frac{40.8}{5}$ $\newline$ Variance = $8.16$ $\newline$ Round it to the nearest tenth and we get $8.2$

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