In the data set below, what is the variance? 5, 1, 8, 5, 4, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Subtract and Square: Now, subtract the mean from each data point and square the result. (5 - 4.5)^2 + (1 - 4.5)^2 + (8 - 4.5)^2 + (5 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2 = (0.5)^2 + (-3.5)^2 + (3.5)^2 + (0.5)^2 + (-0.5)^2 + (-0.5)^2 = 0.25 + 12.25 + 12.25 + 0.25 + 0.25 + 0.25 = 25.5Calculate Sum of Squared Differences: Finally, divide the sum of squared differences by the number of data points to find the variance. Variance (σ^2) = 25.5 / 6 Variance (σ^2) = 4.25 Round to the nearest tenth. Variance (σ^2) ≈ 4.3

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In the data set below, what is the variance? $\newline$ $5, 1, 8, 5, 4, 4$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Algebra 1

Variance and standard deviation

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Q. In the data set below, what is the variance?

\newline

5, 1, 8, 5, 4, 4

\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. $\newline$ $(5 - 4.5)^2 + (1 - 4.5)^2 + (8 - 4.5)^2 + (5 - 4.5)^2 + (4 - 4.5)^2 + (4 - 4.5)^2$ $\newline$ = $(0.5)^2 + (-3.5)^2 + (3.5)^2 + (0.5)^2 + (-0.5)^2 + (-0.5)^2$ $\newline$ = $0.25 + 12.25 + 12.25 + 0.25 + 0.25 + 0.25$ $\newline$ = $25.5$
Calculate Sum of Squared Differences: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{25.5}{6}$ $\newline$ Variance $\sigma^2$ = $4$ . $25$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 4.3$