In the data set below, what is the variance? 9, 4, 9, 4, 6, 1 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate squared differences: Now, calculate the squared differences from the mean for each data point. (9 - 5.5)^2 + (4 - 5.5)^2 + (9 - 5.5)^2 + (4 - 5.5)^2 + (6 - 5.5)^2 + (1 - 5.5)^2 = (3.5)^2 + (-1.5)^2 + (3.5)^2 + (-1.5)^2 + (0.5)^2 + (-4.5)^2 = 12.25 + 2.25 + 12.25 + 2.25 + 0.25 + 20.25 = 49.5Find the 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 = 49.5 / 6 σ^2 = 8.25 Since we need to round to the nearest tenth, σ^2 ≈ 8.3

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In the data set below, what is the variance? $\newline$ $9, 4, 9, 4, 6, 1$ $\newline$ 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

9, 4, 9, 4, 6, 1

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate squared differences: Now, calculate the squared differences from the mean for each data point. $\newline$ $(9 - 5.5)^2 + (4 - 5.5)^2 + (9 - 5.5)^2 + (4 - 5.5)^2 + (6 - 5.5)^2 + (1 - 5.5)^2$ $\newline$ = $(3.5)^2 + (-1.5)^2 + (3.5)^2 + (-1.5)^2 + (0.5)^2 + (-4.5)^2$ $\newline$ = $12.25 + 2.25 + 12.25 + 2.25 + 0.25 + 20.25$ $\newline$ = $49.5$
Find the variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{49.5}{6}$ $\newline$ $\sigma^2 = 8.25$ $\newline$ Since we need to round to the nearest tenth, $\sigma^2 \approx 8.3$