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In the data set below, what is the variance? $\newline$ $8, 8, 9, 6, 4, 7$ $\newline$ 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

8, 8, 9, 6, 4, 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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (8 - 7)^2 + (8 - 7)^2 + (9 - 7)^2 + (6 - 7)^2 + (4 - 7)^2 + (7 - 7)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (1)^2 + (1)^2 + (2)^2 + (-1)^2 + (-3)^2 + (0)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 1 + 1 + 4 + 1 + 9 + 0$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 16$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{16}{6}$ $\newline$ Variance $\sigma^2$ = $2$ . $666$ ... $\newline$ Rounded to the nearest tenth, Variance $\sigma^2$ $\approx 2.7$

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