In the data set below, what is the variance? 7, 6, 2, 8, 8, 5 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now that we have the mean, we calculate the squared differences from the mean for each data point. (7 - 6)^2 + (6 - 6)^2 + (2 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (5 - 6)^2 = (1)^2 + (0)^2 + (-4)^2 + (2)^2 + (2)^2 + (-1)^2 = 1 + 0 + 16 + 4 + 4 + 1 = 26Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. Σ(x_i - μ)^2 = 26 N = 6 Variance σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 26/6 σ^2 ≈ 4.333... Rounded to the nearest tenth: σ^2 ≈ 4.3

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In the data set below, what is the variance? $\newline$ $7, 6, 2, 8, 8, 5$ $\newline$ 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

7, 6, 2, 8, 8, 5

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now that we have the mean, we calculate the squared differences from the mean for each data point. $\newline$ $(7 - 6)^2 + (6 - 6)^2 + (2 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 + (5 - 6)^2$ $\newline$ = $(1)^2 + (0)^2 + (-4)^2 + (2)^2 + (2)^2 + (-1)^2$ $\newline$ = $1 + 0 + 16 + 4 + 4 + 1$ $\newline$ = $26$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\Sigma(x_i - \mu)^2 = 26$ $\newline$ $N = 6$ $\newline$ Variance $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 26/6$ $\newline$ $\sigma^2 \approx 4.333...$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 4.3$