In the data set below, what is the variance? 8, 7, 4, 9, 6, 8 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (8 - 7)^2 + (7 - 7)^2 + (4 - 7)^2 + (9 - 7)^2 + (6 - 7)^2 + (8 - 7)^2 = (1)^2 + (0)^2 + (-3)^2 + (2)^2 + (-1)^2 + (1)^2 = 1 + 0 + 9 + 4 + 1 + 1 = 16Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. σ^2 = Σ(x_i - μ)^2 / N σ^2 = 16 / 6 σ^2 ≈ 2.6667 Round the variance to the nearest tenth. σ^2 ≈ 2.7

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In the data set below, what is the variance? $\newline$ $8, 7, 4, 9, 6, 8$ $\newline$ 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

8, 7, 4, 9, 6, 8

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (8 - 7)^2 + (7 - 7)^2 + (4 - 7)^2 + (9 - 7)^2 + (6 - 7)^2 + (8 - 7)^2$ $\newline$ $= (1)^2 + (0)^2 + (-3)^2 + (2)^2 + (-1)^2 + (1)^2$ $\newline$ $= 1 + 0 + 9 + 4 + 1 + 1$ $\newline$ $= 16$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{16}{6}$ $\newline$ $\sigma^2 \approx 2.6667$ $\newline$ Round the variance to the nearest tenth. $\newline$ $\sigma^2 \approx 2.7$