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In the data set below, what is the variance? $\newline$ $3, 3, 1, 1, 6, 7$ $\newline$ 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

3, 3, 1, 1, 6, 7

\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. $\newline$ $(3 - 3.5)^2 + (3 - 3.5)^2 + (1 - 3.5)^2 + (1 - 3.5)^2 + (6 - 3.5)^2 + (7 - 3.5)^2$ $\newline$ = $(0.5)^2 + (0.5)^2 + (-2.5)^2 + (-2.5)^2 + (2.5)^2 + (3.5)^2$ $\newline$ = $0.25 + 0.25 + 6.25 + 6.25 + 6.25 + 12.25$ $\newline$ = $31.5$
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 $\sigma^2$ = $\frac{31.5}{6}$ $\newline$ Variance $\sigma^2$ = $5$ . $25$ $\newline$ Since we need to round to the nearest tenth, the variance is $5.3$ .

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