In the data set below, what is the variance? 2, 1, 9, 2, 8, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. (2 - 4)^2 + (1 - 4)^2 + (9 - 4)^2 + (2 - 4)^2 + (8 - 4)^2 + (2 - 4)^2 = (-2)^2 + (-3)^2 + (5)^2 + (-2)^2 + (4)^2 + (-2)^2 = 4 + 9 + 25 + 4 + 16 + 4 = 62Find Variance: Finally, we'll divide the sum of squared differences by the number of data points to find the variance. Variance (σ^2) = Sum of squared differences / Number of data points Variance (σ^2) = 62 / 6 Variance (σ^2) = 10.333... Rounded to the nearest tenth, Variance (σ^2) ≈ 10.3

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In the data set below, what is the variance? $\newline$ $2, 1, 9, 2, 8, 2$ $\newline$ 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

2, 1, 9, 2, 8, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $(2 - 4)^2 + (1 - 4)^2 + (9 - 4)^2 + (2 - 4)^2 + (8 - 4)^2 + (2 - 4)^2$ $\newline$ = $(-2)^2 + (-3)^2 + (5)^2 + (-2)^2 + (4)^2 + (-2)^2$ $\newline$ = $4 + 9 + 25 + 4 + 16 + 4$ $\newline$ = $62$
Find Variance: Finally, we'll 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 $\sigma^2$ = $\frac{62}{6}$ $\newline$ Variance $\sigma^2$ = $10$ . $333$ ... $\newline$ Rounded to the nearest tenth, Variance $\sigma^2$ $\approx 10.3$