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In the data set below, what is the variance? $\newline$ $8, 3, 4, 6, 3$ $\newline$ 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, 4, 6, 3

\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, $(8 - 4.8)^2 + (3 - 4.8)^2 + (4 - 4.8)^2 + (6 - 4.8)^2 + (3 - 4.8)^2$ $\newline$ That's $(3.2)^2 + (-1.8)^2 + (-0.8)^2 + (1.2)^2 + (-1.8)^2$ $\newline$ Which is $10.24 + 3.24 + 0.64 + 1.44 + 3.24$ $\newline$ Add 'em up, and we get $18.8$
Sum of Squares: Alright, almost there. $\newline$ We divide that sum by the number of values, which is $5$ . $\newline$ Variance ( $\sigma^2$ ) = $\frac{18.8}{5}$ $\newline$ Variance ( $\sigma^2$ ) = $3.76$ $\newline$ Round it to the nearest tenth, and we get $3.8$

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