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In the data set below, what is the variance? $\newline$ $8, 9, 5, 1, 3, 8, 8$ $\newline$ 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, 9, 5, 1, 3, 8, 8

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (8 - 6)^2 + (9 - 6)^2 + (5 - 6)^2 + (1 - 6)^2 + (3 - 6)^2 + (8 - 6)^2 + (8 - 6)^2$ $\newline$ $= (2)^2 + (3)^2 + (-1)^2 + (-5)^2 + (-3)^2 + (2)^2 + (2)^2$ $\newline$ $= 4 + 9 + 1 + 25 + 9 + 4 + 4$ $\newline$ $= 56$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 7$ (number of data points) $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{56}{7}$ $\newline$ $\sigma^2 = 8$
Round to Nearest Tenth: Round the variance to the nearest tenth, if necessary. In this case, the variance is a whole number, so no rounding is needed.

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