In the data set below, what is the variance? 8, 8, 7, 5, 9, 4, 8 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 = (8 + 8 + 7 + 5 + 9 + 4 + 8)/7 μ = 49/7 μ = 7Calculate Squared Differences: Data set: 8, 8, 7, 5, 9, 4, 8 μ = 7 Calculate the sum of the squared differences from the mean. (8 - 7)^2 + (8 - 7)^2 + (7 - 7)^2 + (5 - 7)^2 + (9 - 7)^2 + (4 - 7)^2 + (8 - 7)^2 = (1)^2 + (1)^2 + (0)^2 + (-2)^2 + (2)^2 + (-3)^2 + (1)^2 = 1 + 1 + 0 + 4 + 4 + 9 + 1 = 20Calculate Variance: We know: Σ(x_i - μ)^2= 20 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 20/7 σ^2 ≈ 2.857 Round to the nearest tenth: σ^2 ≈ 2.9

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In the data set below, what is the variance? $\newline$ $8, 8, 7, 5, 9, 4, 8$ $\newline$ 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

8, 8, 7, 5, 9, 4, 8

\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 = $(8 + 8 + 7 + 5 + 9 + 4 + 8)/7$ $\newline$ $\mu = 49/7$ $\newline$ $\mu = 7$
Calculate Squared Differences: Data set: $8, 8, 7, 5, 9, 4, 8$
$\mu = 7$
Calculate the sum of the squared differences from the mean.
$(8 - 7)^2 + (8 - 7)^2 + (7 - 7)^2 + (5 - 7)^2 + (9 - 7)^2 + (4 - 7)^2 + (8 - 7)^2$
$= (1)^2 + (1)^2 + (0)^2 + (-2)^2 + (2)^2 + (-3)^2 + (1)^2$
$= 1 + 1 + 0 + 4 + 4 + 9 + 1$
$= 20$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 20$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{20}{7}$ $\newline$ $\sigma^2 \approx 2.857$ $\newline$ Round to the nearest tenth: $\sigma^2 \approx 2.9$