In the data set below, what is the variance? 5, 2, 7, 7, 5, 8, 8 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. (5 - 6)^2 + (2 - 6)^2 + (7 - 6)^2 + (7 - 6)^2 + (5 - 6)^2 + (8 - 6)^2 + (8 - 6)^2 = (-1)^2 + (-4)^2 + (1)^2 + (1)^2 + (-1)^2 + (2)^2 + (2)^2 = 1 + 16 + 1 + 1 + 1 + 4 + 4 = 28Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. Number of data points N = 7 Variance σ^2 = Σ(x_i - μ)^2 / N σ^2 = 28/7 σ^2 = 4 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? $\newline$ $5, 2, 7, 7, 5, 8, 8$ $\newline$ 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, 2, 7, 7, 5, 8, 8

\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. $\newline$ $(5 - 6)^2 + (2 - 6)^2 + (7 - 6)^2 + (7 - 6)^2 + (5 - 6)^2 + (8 - 6)^2 + (8 - 6)^2$ $\newline$ = $(-1)^2 + (-4)^2 + (1)^2 + (1)^2 + (-1)^2 + (2)^2 + (2)^2$ $\newline$ = $1 + 16 + 1 + 1 + 1 + 4 + 4$ $\newline$ = $28$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ Number of data points $N = 7$ $\newline$ Variance $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{28}{7}$ $\newline$ $\sigma^2 = 4$ $\newline$ Since the variance is a whole number, there is no need to round to the nearest tenth.