In the data set below, what is the variance? 1, 7, 4, 7, 9 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (1 - 5.6)^2 + (7 - 5.6)^2 + (4 - 5.6)^2 + (7 - 5.6)^2 + (9 - 5.6)^2 = (-4.6)^2 + (1.4)^2 + (-1.6)^2 + (1.4)^2 + (3.4)^2 = 21.16 + 1.96 + 2.56 + 1.96 + 11.56 = 39.2Find 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 = 39.2 / 5 σ^2 = 7.84 Round the variance to the nearest tenth. σ^2 ≈ 7.8

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In the data set below, what is the variance? $\newline$ $1, 7, 4, 7, 9$ $\newline$ 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

1, 7, 4, 7, 9

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\Sigma(x_i - \mu)^2 = (1 - 5.6)^2 + (7 - 5.6)^2 + (4 - 5.6)^2 + (7 - 5.6)^2 + (9 - 5.6)^2$ = $(-4.6)^2 + (1.4)^2 + (-1.6)^2 + (1.4)^2 + (3.4)^2$ = $21.16 + 1.96 + 2.56 + 1.96 + 11.56$ = $39.2$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{39.2}{5}$ $\newline$ $\sigma^2 = 7.84$ $\newline$ Round the variance to the nearest tenth. $\newline$ $\sigma^2 \approx 7.8$