In the data set below, what is the variance? 6, 3, 2, 3, 9, 7 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean. (6 - 5)^2 + (3 - 5)^2 + (2 - 5)^2 + (3 - 5)^2 + (9 - 5)^2 + (7 - 5)^2 = 1^2 + (-2)^2 + (-3)^2 + (-2)^2 + 4^2 + 2^2 = 1 + 4 + 9 + 4 + 16 + 4 = 38Find Variance: Finally, we 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) = 38 / 6 Variance (σ^2) = 6.333... Rounded to the nearest tenth, Variance (σ^2) ≈ 6.3

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In the data set below, what is the variance? $\newline$ $6, 3, 2, 3, 9, 7$ $\newline$ 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

6, 3, 2, 3, 9, 7

\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. $\newline$ $(6 - 5)^2 + (3 - 5)^2 + (2 - 5)^2 + (3 - 5)^2 + (9 - 5)^2 + (7 - 5)^2$ $\newline$ $= 1^2 + (-2)^2 + (-3)^2 + (-2)^2 + 4^2 + 2^2$ $\newline$ $= 1 + 4 + 9 + 4 + 16 + 4$ $\newline$ $= 38$
Find Variance: Finally, we 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 $\sigma^2$ = $\frac{38}{6}$ $\newline$ Variance $\sigma^2$ = $6.333\ldots$ $\newline$ Rounded to the nearest tenth, Variance $\sigma^2$ $\approx 6.3$