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

\newline

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

\newline

variance

(\sigma^2)

: _____

Subtract and Square: Now, subtract the mean from each data point and square the result. $\newline$ $(8 - 5.6)^2 = (2.4)^2 = 5.76$ $\newline$ $(3 - 5.6)^2 = (-2.6)^2 = 6.76$ $\newline$ $(3 - 5.6)^2 = (-2.6)^2 = 6.76$ $\newline$ $(9 - 5.6)^2 = (3.4)^2 = 11.56$ $\newline$ $(5 - 5.6)^2 = (-0.6)^2 = 0.36$
Add Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $5.76 + 6.76 + 6.76 + 11.56 + 0.36$ $\newline$ Sum of squared differences = $31.2$
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 $\sigma^2$ = $\frac{31.2}{5}$ $\newline$ Variance $\sigma^2$ = $6$ . $24$
Round to Nearest Tenth: Round the variance to the nearest tenth. Variance $\sigma^2$ $\approx 6.2$

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