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In the data set below, what is the variance? $\newline$ $1, 9, 4, 7, 8$ $\newline$ 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, 4, 7, 8

\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 $(\text{each number} - \text{mean})^2$ . $\newline$ So, $(1 - 5.8)^2 + (9 - 5.8)^2 + (4 - 5.8)^2 + (7 - 5.8)^2 + (8 - 5.8)^2$ $\newline$ That's $(4.8)^2 + (3.2)^2 + (1.8)^2 + (1.2)^2 + (2.2)^2$ $\newline$ Which is $23.04 + 10.24 + 3.24 + 1.44 + 4.84$ $\newline$ Add 'em up, and we get $42.8$
Sum of Squares: Last step, divide that sum by the number of data points, which is $5$ . $\newline$ Variance ( $\sigma^2$ ) = $\frac{42.8}{5}$ $\newline$ Variance ( $\sigma^2$ ) = $8.56$ $\newline$ Round it to the nearest tenth, and we get $8.6$

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