In the data set below, what is the variance? 7, 5, 4, 6, 4, 1, 1 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 = (7 + 5 + 4 + 6 + 4 + 1 + 1)/7 μ = 28/7 μ = 4Calculate Squared Differences: Data set: 7, 5, 4, 6, 4, 1, 1 μ = 4 Calculate the sum of the squared differences from the mean, Σ(x_i - μ)^2. (7 - 4)^2 + (5 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (1 - 4)^2 + (1 - 4)^2 = (3)^2 + (1)^2 + (0)^2 + (2)^2 + (0)^2 + (-3)^2 + (-3)^2 = 9 + 1 + 0 + 4 + 0 + 9 + 9 = 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? $\newline$ $7, 5, 4, 6, 4, 1, 1$ $\newline$ 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

7, 5, 4, 6, 4, 1, 1

\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 = $(7 + 5 + 4 + 6 + 4 + 1 + 1)/7$ $\newline$ $\mu = 28/7$ $\newline$ $\mu = 4$
Calculate Squared Differences: Data set: $7, 5, 4, 6, 4, 1, 1$
$\mu = 4$
Calculate the sum of the squared differences from the mean, $\Sigma(x_i - \mu)^2$ .
$(7 - 4)^2 + (5 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (4 - 4)^2 + (1 - 4)^2 + (1 - 4)^2$
$= (3)^2 + (1)^2 + (0)^2 + (2)^2 + (0)^2 + (-3)^2 + (-3)^2$
$= 9 + 1 + 0 + 4 + 0 + 9 + 9$
$= 32$
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: $\sigma^2 \approx 4.6$