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

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. Σ(x_i - mean)^2 = (2 - 3)^2 + (2 - 3)^2 + (1 - 3)^2 + (8 - 3)^2 + (4 - 3)^2 + (3 - 3)^2 + (1 - 3)^2 Σ(x_i - mean)^2 = (-1)^2 + (-1)^2 + (-2)^2 + (5)^2 + (1)^2 + (0)^2 + (-2)^2 Σ(x_i - mean)^2 = 1 + 1 + 4 + 25 + 1 + 0 + 4 Σ(x_i - mean)^2 = 36Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. Variance (σ^2) = Σ(x_i - mean)^2 / N Variance (σ^2) = 36 / 7 Variance (σ^2) ≈ 5.1 (rounded to the nearest tenth)

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In the data set below, what is the variance? $\newline$ $2, 2, 1, 8, 4, 3, 1$ $\newline$ 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

2, 2, 1, 8, 4, 3, 1

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (2 - 3)^2 + (2 - 3)^2 + (1 - 3)^2 + (8 - 3)^2 + (4 - 3)^2 + (3 - 3)^2 + (1 - 3)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (-1)^2 + (-1)^2 + (-2)^2 + (5)^2 + (1)^2 + (0)^2 + (-2)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 1 + 1 + 4 + 25 + 1 + 0 + 4$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 36$
Find Variance: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{36}{7}$ $\newline$ Variance $\sigma^2$ $\approx 5.1$ (rounded to the nearest tenth)