In the data set below, what is the variance? 7, 1, 5, 2, 5, 5, 3 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 - 4)^2 + (1 - 4)^2 + (5 - 4)^2 + (2 - 4)^2 + (5 - 4)^2 + (5 - 4)^2 + (3 - 4)^2 = 3^2 + (-3)^2 + 1^2 + (-2)^2 + 1^2 + 1^2 + (-1)^2 = 9 + 9 + 1 + 4 + 1 + 1 + 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 = 7 Variance σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 26/7 σ^2 ≈ 3.71428571429 Rounded to the nearest tenth: σ^2 ≈ 3.7

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In the data set below, what is the variance? $\newline$ $7, 1, 5, 2, 5, 5, 3$ $\newline$ 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, 1, 5, 2, 5, 5, 3

\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. $\newline$ $(7 - 4)^2 + (1 - 4)^2 + (5 - 4)^2 + (2 - 4)^2 + (5 - 4)^2 + (5 - 4)^2 + (3 - 4)^2$ $\newline$ $= 3^2 + (-3)^2 + 1^2 + (-2)^2 + 1^2 + 1^2 + (-1)^2$ $\newline$ $= 9 + 9 + 1 + 4 + 1 + 1 + 1$ $\newline$ $= 26$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\Sigma(x_i - \mu)^2 = 26$ $\newline$ $N = 7$ $\newline$ Variance $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 26/7$ $\newline$ $\sigma^2 \approx 3.71428571429$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 3.7$