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In the data set below, what is the variance? $\newline$ $9, 4, 3, 3, 9, 7, 7$ $\newline$ 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

9, 4, 3, 3, 9, 7, 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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (9 - 6)^2 + (4 - 6)^2 + (3 - 6)^2 + (3 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (7 - 6)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 3^2 + (-2)^2 + (-3)^2 + (-3)^2 + 3^2 + 1^2 + 1^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 9 + 4 + 9 + 9 + 9 + 1 + 1$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 42$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{42}{7}$ $\newline$ Variance $\sigma^2$ = $6$

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