In the data set below, what is the variance? 2, 3, 8, 2, 1, 6, 6 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. (2 - 4)^2 + (3 - 4)^2 + (8 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (6 - 4)^2 + (6 - 4)^2 = (-2)^2 + (-1)^2 + (4)^2 + (-2)^2 + (-3)^2 + (2)^2 + (2)^2 = 4 + 1 + 16 + 4 + 9 + 4 + 4 = 42Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. Σ(x_i - μ)^2 = 42 N = 7 Variance σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 42/7 σ^2 = 6 Since the variance is a whole number, there is no need to round to the nearest tenth.

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In the data set below, what is the variance? $\newline$ $2, 3, 8, 2, 1, 6, 6$ $\newline$ 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, 3, 8, 2, 1, 6, 6

\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. $\newline$ $(2 - 4)^2 + (3 - 4)^2 + (8 - 4)^2 + (2 - 4)^2 + (1 - 4)^2 + (6 - 4)^2 + (6 - 4)^2$ $\newline$ = $(-2)^2 + (-1)^2 + (4)^2 + (-2)^2 + (-3)^2 + (2)^2 + (2)^2$ $\newline$ = $4 + 1 + 16 + 4 + 9 + 4 + 4$ $\newline$ = $42$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\Sigma(x_i - \mu)^2 = 42$ $\newline$ $N = 7$ $\newline$ Variance $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 42/7$ $\newline$ $\sigma^2 = 6$ $\newline$ Since the variance is a whole number, there is no need to round to the nearest tenth.