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In the data set below, what is the variance? $\newline$ $7, 6, 5, 5, 5, 5$ $\newline$ 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

7, 6, 5, 5, 5, 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. $\newline$ $(7 - 5.5)^2 = (1.5)^2 = 2.25$ $\newline$ $(6 - 5.5)^2 = (0.5)^2 = 0.25$ $\newline$ $(5 - 5.5)^2 = (-0.5)^2 = 0.25$ $\newline$ $(5 - 5.5)^2 = (-0.5)^2 = 0.25$ $\newline$ $(5 - 5.5)^2 = (-0.5)^2 = 0.25$ $\newline$ $(5 - 5.5)^2 = (-0.5)^2 = 0.25$
Add Squared Differences: Add up all the squared differences. $\newline$ Sum of squared differences = $2.25 + 0.25 + 0.25 + 0.25 + 0.25 + 0.25$ $\newline$ Sum of squared differences = $3.5$
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 $\sigma^2$ = $\frac{3.5}{6}$ $\newline$ Variance $\sigma^2$ = $0$ . $583333$ ...
Round to Nearest Tenth: Round the variance to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 0.6$

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