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In the data set below, what is the variance? $\newline$ $9, 9, 9, 4, 1$ $\newline$ 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, 9, 9, 4, 1

\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. $\newline$ $(9 - 6.4)^2 = (2.6)^2 = 6.76$ $\newline$ $(9 - 6.4)^2 = (2.6)^2 = 6.76$ $\newline$ $(9 - 6.4)^2 = (2.6)^2 = 6.76$ $\newline$ $(4 - 6.4)^2 = (-2.4)^2 = 5.76$ $\newline$ $(1 - 6.4)^2 = (-5.4)^2 = 29.16$
Add Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $6.76 + 6.76 + 6.76 + 5.76 + 29.16$ $\newline$ Sum of squared differences = $55.2$
Calculate Variance: Divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{55.2}{5}$ $\newline$ Variance $\sigma^2$ = $11.04$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 11.0$

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