In the data set below, what is the variance? 3, 1, 1, 8, 1, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum Squared Differences: Now, we will calculate the sum of the squared differences from the mean for each data point. Σ(x_i - μ)^2 = (3 - 3)^2 + (1 - 3)^2 + (1 - 3)^2 + (8 - 3)^2 + (1 - 3)^2 + (4 - 3)^2 = 0^2 + (-2)^2 + (-2)^2 + 5^2 + (-2)^2 + 1^2 = 0 + 4 + 4 + 25 + 4 + 1 = 38Find Variance: Finally, we will divide the sum of squared differences by the number of data points to find the variance. Number of data points N = 6 Variance σ^2 = Σ(x_i - μ)^2 / N σ^2 = 38/6 σ^2 ≈ 6.333... Rounded to the nearest tenth, σ^2 ≈ 6.3

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In the data set below, what is the variance? $\newline$ $3, 1, 1, 8, 1, 4$ $\newline$ 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

3, 1, 1, 8, 1, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, we will calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (3 - 3)^2 + (1 - 3)^2 + (1 - 3)^2 + (8 - 3)^2 + (1 - 3)^2 + (4 - 3)^2$ $\newline$ $= 0^2 + (-2)^2 + (-2)^2 + 5^2 + (-2)^2 + 1^2$ $\newline$ $= 0 + 4 + 4 + 25 + 4 + 1$ $\newline$ $= 38$
Find Variance: Finally, we will divide the sum of squared differences by the number of data points to find the variance. $\newline$ Number of data points $N = 6$ $\newline$ Variance $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{38}{6}$ $\newline$ $\sigma^2 \approx 6.333...$ $\newline$ Rounded to the nearest tenth, $\sigma^2 \approx 6.3$