In the data set below, what is the variance? 4, 8, 4, 5, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Subtract and Square: Now, subtract the mean from each data point and square the result. (4 - 5)^2 = (-1)^2 = 1 (8 - 5)^2 = (3)^2 = 9 (4 - 5)^2 = (-1)^2 = 1 (5 - 5)^2 = (0)^2 = 0 (4 - 5)^2 = (-1)^2 = 1Sum Squared Differences: Next, sum up all the squared differences. Sum = 1 + 9 + 1 + 0 + 1 Sum = 12Calculate Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. Variance (σ^2) = Sum / N Variance (σ^2) = 12 / 5 Variance (σ^2) = 2.4 Round to the nearest tenth. Variance (σ^2) ≈ 2.4

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

4, 8, 4, 5, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Subtract and Square: Now, subtract the mean from each data point and square the result. $\newline$ $(4 - 5)^2 = (-1)^2 = 1$ $\newline$ $(8 - 5)^2 = (3)^2 = 9$ $\newline$ $(4 - 5)^2 = (-1)^2 = 1$ $\newline$ $(5 - 5)^2 = (0)^2 = 0$ $\newline$ $(4 - 5)^2 = (-1)^2 = 1$
Sum Squared Differences: Next, sum up all the squared differences. $\newline$ Sum = $1 + 9 + 1 + 0 + 1$ $\newline$ Sum = $12$
Calculate Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = $\frac{\text{Sum}}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{12}{5}$ $\newline$ Variance $\sigma^2$ = $2$ . $4$ $\newline$ Round to the nearest tenth. $\newline$ Variance $\sigma^2$ $\approx 2.4$