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In the data set below, what is the variance? $\newline$ $6, 2, 1, 3, 4, 4, 1$ $\newline$ 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

6, 2, 1, 3, 4, 4, 1

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean for each data point. $\newline$ $(6 - 3)^2 = 9$ $\newline$ $(2 - 3)^2 = 1$ $\newline$ $(1 - 3)^2 = 4$ $\newline$ $(3 - 3)^2 = 0$ $\newline$ $(4 - 3)^2 = 1$ $\newline$ $(4 - 3)^2 = 1$ $\newline$ $(1 - 3)^2 = 4$
Sum Up Squared Differences: Next, sum up all the squared differences. $\newline$ Sum = $9 + 1 + 4 + 0 + 1 + 1 + 4$ $\newline$ Sum = $20$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{\text{Sum}}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{20}{7}$ $\newline$ Variance $\sigma^2$ $\approx 2.9$ when rounded to the nearest tenth.

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