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

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Variance and standard deviation

Full solution

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

\newline

9, 3, 3, 6, 9

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, subtract the mean from each data point and square the result. $\newline$ $(9 - 6)^2 = 3^2 = 9$ $\newline$ $(3 - 6)^2 = (-3)^2 = 9$ $\newline$ $(3 - 6)^2 = (-3)^2 = 9$ $\newline$ $(6 - 6)^2 = 0^2 = 0$ $\newline$ $(9 - 6)^2 = 3^2 = 9$
Sum of Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $9 + 9 + 9 + 0 + 9$ $\newline$ Sum of squared differences = $36$
Calculate Variance: 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 $\sigma^2$ = $\frac{36}{5}$ $\newline$ Variance $\sigma^2$ = $7$ . $2$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 7.2$

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