In the data set below, what is the variance? 4, 7, 9, 4, 3, 7, 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 = (4 + 7 + 9 + 4 + 3 + 7 + 8)/7 μ = 42/7 μ = 6Calculate Sum of Squared Differences: Data set: 4, 7, 9, 4, 3, 7, 8 μ = 6 Calculate the sum of the squared differences from the mean, Σ(x_i - μ)^2. (4 - 6)^2 + (7 - 6)^2 + (9 - 6)^2 + (4 - 6)^2 + (3 - 6)^2 + (7 - 6)^2 + (8 - 6)^2 = (-2)^2 + (1)^2 + (3)^2 + (-2)^2 + (-3)^2 + (1)^2 + (2)^2 = 4 + 1 + 9 + 4 + 9 + 1 + 4 = 32Calculate Variance: We know: Σ(x_i - μ)^2= 32 N= 7 Calculate the variance and round your answer to the nearest tenth. σ^2 = (Σ(x_i - μ)^2)/N σ^2 = 32/7 σ^2 ≈ 4.57142857 Rounded to the nearest tenth: σ^2 ≈ 4.6

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In the data set below, what is the variance? $\newline$ $4, 7, 9, 4, 3, 7, 8$ $\newline$ 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

4, 7, 9, 4, 3, 7, 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 = $(4 + 7 + 9 + 4 + 3 + 7 + 8)/7$ $\newline$ $\mu = 42/7$ $\newline$ $\mu = 6$
Calculate Sum of Squared Differences: Data set: $4, 7, 9, 4, 3, 7, 8$
$\mu = 6$
Calculate the sum of the squared differences from the mean, $\Sigma(x_i - \mu)^2$ .
$(4 - 6)^2 + (7 - 6)^2 + (9 - 6)^2 + (4 - 6)^2 + (3 - 6)^2 + (7 - 6)^2 + (8 - 6)^2$
$= (-2)^2 + (1)^2 + (3)^2 + (-2)^2 + (-3)^2 + (1)^2 + (2)^2$
$= 4 + 1 + 9 + 4 + 9 + 1 + 4$
$= 32$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 32$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{32}{7}$ $\newline$ $\sigma^2 \approx 4.57142857$ $\newline$ Rounded to the nearest tenth: $\sigma^2 \approx 4.6$