In the data set below, what is the variance? 9, 5, 5, 2, 2, 5, 7 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 = (9 + 5 + 5 + 2 + 2 + 5 + 7)/7 μ = 35/7 μ = 5Calculate Squared Differences: Data set: 9, 5, 5, 2, 2, 5, 7 μ = 5 Calculate the sum of the squared differences from the mean. (9 - 5)^2 + (5 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (2 - 5)^2 + (5 - 5)^2 + (7 - 5)^2 = (4)^2 + (0)^2 + (0)^2 + (-3)^2 + (-3)^2 + (0)^2 + (2)^2 = 16 + 0 + 0 + 9 + 9 + 0 + 4 = 38Calculate Variance: We know: Σ(x_i - μ)^2= 38 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 38/7 σ^2 ≈ 5.4 (rounded to the nearest tenth)

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In the data set below, what is the variance? $\newline$ $9, 5, 5, 2, 2, 5, 7$ $\newline$ 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

9, 5, 5, 2, 2, 5, 7

\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 = $(9 + 5 + 5 + 2 + 2 + 5 + 7)/7$ $\newline$ $\mu = 35/7$ $\newline$ $\mu = 5$
Calculate Squared Differences: Data set: $9, 5, 5, 2, 2, 5, 7$
$\mu = 5$
Calculate the sum of the squared differences from the mean.
$(9 - 5)^2 + (5 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (2 - 5)^2 + (5 - 5)^2 + (7 - 5)^2$
$= (4)^2 + (0)^2 + (0)^2 + (-3)^2 + (-3)^2 + (0)^2 + (2)^2$
$= 16 + 0 + 0 + 9 + 9 + 0 + 4$
$= 38$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 38$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 38/7$ $\newline$ $\sigma^2 \approx 5.4$ (rounded to the nearest tenth)