In the data set below, what is the variance? 5, 1, 6, 4, 9, 2 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 = (5 - 4.5)^2 + (1 - 4.5)^2 + (6 - 4.5)^2 + (4 - 4.5)^2 + (9 - 4.5)^2 + (2 - 4.5)^2 Σ(x_i - mean)^2 = (0.5)^2 + (-3.5)^2 + (1.5)^2 + (-0.5)^2 + (4.5)^2 + (-2.5)^2 Σ(x_i - mean)^2 = 0.25 + 12.25 + 2.25 + 0.25 + 20.25 + 6.25 Σ(x_i - mean)^2 = 41.5Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. Variance (σ^2) = Σ(x_i - mean)^2 / N Variance (σ^2) = 41.5 / 6 Variance (σ^2) = 6.916666... Rounded to the nearest tenth, Variance (σ^2) ≈ 6.9

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In the data set below, what is the variance? $\newline$ $5, 1, 6, 4, 9, 2$ $\newline$ 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, 1, 6, 4, 9, 2

\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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (5 - 4.5)^2 + (1 - 4.5)^2 + (6 - 4.5)^2 + (4 - 4.5)^2 + (9 - 4.5)^2 + (2 - 4.5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (0.5)^2 + (-3.5)^2 + (1.5)^2 + (-0.5)^2 + (4.5)^2 + (-2.5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 0.25 + 12.25 + 2.25 + 0.25 + 20.25 + 6.25$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 41.5$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{41.5}{6}$ $\newline$ Variance $\sigma^2$ = $6$ . $916666$ ... $\newline$ Rounded to the nearest tenth, Variance $\sigma^2$ $\approx 6.9$