In the data set below, what is the variance? 5, 6, 3, 6, 4, 9, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. Σ(x_i - mean)^2 = (5 - 5)^2 + (6 - 5)^2 + (3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (2 - 5)^2 Σ(x_i - mean)^2 = 0^2 + 1^2 + (-2)^2 + 1^2 + (-1)^2 + 4^2 + (-3)^2 Σ(x_i - mean)^2 = 0 + 1 + 4 + 1 + 1 + 16 + 9 Σ(x_i - mean)^2 = 32Find 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) = 32 / 7 Variance (σ^2) ≈ 4.6 when rounded to the nearest tenth.

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In the data set below, what is the variance? $\newline$ $5, 6, 3, 6, 4, 9, 2$ $\newline$ 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

5, 6, 3, 6, 4, 9, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (5 - 5)^2 + (6 - 5)^2 + (3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (2 - 5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 0^2 + 1^2 + (-2)^2 + 1^2 + (-1)^2 + 4^2 + (-3)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 0 + 1 + 4 + 1 + 1 + 16 + 9$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 32$
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 $\sigma^2$ = $\frac{32}{7}$ $\newline$ Variance $\sigma^2$ $\approx 4.6$ when rounded to the nearest tenth.