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In the data set below, what is the variance? $\newline$ $8, 1, 3, 3, 1, 2$ $\newline$ 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, 1, 3, 3, 1, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (8 - 3)^2 + (1 - 3)^2 + (3 - 3)^2 + (3 - 3)^2 + (1 - 3)^2 + (2 - 3)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 25 + 4 + 0 + 0 + 4 + 1$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 34$
Find Variance: Finally, we'll 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 $\sigma^2$ = $\frac{34}{6}$ $\newline$ variance $\sigma^2$ = $5$ . $666$ ... $\newline$ Rounded to the nearest tenth, variance $\sigma^2$ $\approx 5.7$

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