In the data set below, what is the variance? 6, 7, 1, 4, 4, 4, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Mean: Calculate the mean of the data set. Mean = (6 + 7 + 1 + 4 + 4 + 4 + 2)/7 μ = 28/7 μ = 4Calculate Squared Differences: Data set: 6, 7, 1, 4, 4, 4, 2 μ = 4 Calculate the sum of the squared differences from the mean. (6 - 4)^2 + (7 - 4)^2 + (1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (2 - 4)^2 = (2)^2 + (3)^2 + (-3)^2 + (0)^2 + (0)^2 + (0)^2 + (-2)^2 = 4 + 9 + 9 + 0 + 0 + 0 + 4 = 26Calculate Variance: We know: Σ(x_i - μ)^2= 26 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 26/7 σ^2 ≈ 3.71428571429 Rounded to the nearest tenth: σ^2 ≈ 3.7

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In the data set below, what is the variance? $\newline$ $6, 7, 1, 4, 4, 4, 2$ $\newline$ 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, 7, 1, 4, 4, 4, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Mean: Calculate the mean of the data set. $\newline$ Mean = $(6 + 7 + 1 + 4 + 4 + 4 + 2)/7$ $\newline$ $\mu = 28/7$ $\newline$ $\mu = 4$
Calculate Squared Differences: Data set: $6, 7, 1, 4, 4, 4, 2$ $\newline$ $\mu = 4$ $\newline$ Calculate the sum of the squared differences from the mean. $\newline$ $(6 - 4)^2 + (7 - 4)^2 + (1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (2 - 4)^2$ $\newline$ $= (2)^2 + (3)^2 + (-3)^2 + (0)^2 + (0)^2 + (0)^2 + (-2)^2$ $\newline$ $= 4 + 9 + 9 + 0 + 0 + 0 + 4$ $\newline$ $= 26$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 26$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 26/7$ $\newline$ $\sigma^2 \approx 3.71428571429$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 3.7$