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

Calculate Sum Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (4 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 + (7 - 6)^2 = (-2)^2 + (-2)^2 + (0)^2 + (1)^2 + (2)^2 + (1)^2 = 4 + 4 + 0 + 1 + 4 + 1 = 14Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. N = 6 (number of data points) σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 14/6 σ^2 ≈ 2.333... Round to the nearest tenth. σ^2 ≈ 2.3

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

4, 4, 6, 7, 8, 7

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (4 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 + (7 - 6)^2$ $\newline$ $= (-2)^2 + (-2)^2 + (0)^2 + (1)^2 + (2)^2 + (1)^2$ $\newline$ $= 4 + 4 + 0 + 1 + 4 + 1$ $\newline$ $= 14$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 6$ (number of data points) $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{14}{6}$ $\newline$ $\sigma^2 \approx 2.333...$ $\newline$ Round to the nearest tenth. $\newline$ $\sigma^2 \approx 2.3$