In the data set below, what is the variance? 6, 6, 1, 5, 3 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. (6 - 4.2)^2 + (6 - 4.2)^2 + (1 - 4.2)^2 + (5 - 4.2)^2 + (3 - 4.2)^2 = (1.8)^2 + (1.8)^2 + (-3.2)^2 + (0.8)^2 + (-1.2)^2 = 3.24 + 3.24 + 10.24 + 0.64 + 1.44 = 18.8Find 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 = 18.8 / 5 σ^2 = 3.76 Round the variance to the nearest tenth. σ^2 ≈ 3.8

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In the data set below, what is the variance? $\newline$ $6, 6, 1, 5, 3$ $\newline$ 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

6, 6, 1, 5, 3

\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. $\newline$ $(6 - 4.2)^2 + (6 - 4.2)^2 + (1 - 4.2)^2 + (5 - 4.2)^2 + (3 - 4.2)^2$ $\newline$ = $(1.8)^2 + (1.8)^2 + (-3.2)^2 + (0.8)^2 + (-1.2)^2$ $\newline$ = $3.24 + 3.24 + 10.24 + 0.64 + 1.44$ $\newline$ = $18.8$
Find the variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{18.8}{5}$ $\newline$ $\sigma^2 = 3.76$ $\newline$ Round the variance to the nearest tenth. $\newline$ $\sigma^2 \approx 3.8$