In the data set below, what is the variance? 4, 4, 1, 8, 4, 9, 5 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 = (4 - 5)^2 + (4 - 5)^2 + (1 - 5)^2 + (8 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (5 - 5)^2 Σ(x_i - mean)^2 = (-1)^2 + (-1)^2 + (-4)^2 + (3)^2 + (-1)^2 + (4)^2 + (0)^2 Σ(x_i - mean)^2 = 1 + 1 + 16 + 9 + 1 + 16 + 0 Σ(x_i - mean)^2 = 44Find 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) = 44 / 7 Variance (σ^2) ≈ 6.3 (rounded to the nearest tenth)

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In the data set below, what is the variance? $\newline$ $4, 4, 1, 8, 4, 9, 5$ $\newline$ 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

4, 4, 1, 8, 4, 9, 5

\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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (4 - 5)^2 + (4 - 5)^2 + (1 - 5)^2 + (8 - 5)^2 + (4 - 5)^2 + (9 - 5)^2 + (5 - 5)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (-1)^2 + (-1)^2 + (-4)^2 + (3)^2 + (-1)^2 + (4)^2 + (0)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 1 + 1 + 16 + 9 + 1 + 16 + 0$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 44$
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 $\sigma^2$ = $\frac{44}{7}$ $\newline$ Variance $\sigma^2$ $\approx 6.3$ (rounded to the nearest tenth)