In the data set below, what is the variance? 2, 6, 7, 5, 4, 7, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean. (2 - 5)^2 + (6 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (4 - 5)^2 = (-3)^2 + (1)^2 + (2)^2 + (0)^2 + (-1)^2 + (2)^2 + (-1)^2 = 9 + 1 + 4 + 0 + 1 + 4 + 1 = 20Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. Variance (σ^2) = Sum of squared differences / Number of data points Variance (σ^2) = 20 / 7 Variance (σ^2) ≈ 2.9 when rounded to the nearest tenth.

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In the data set below, what is the variance? $\newline$ $2, 6, 7, 5, 4, 7, 4$ $\newline$ 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

2, 6, 7, 5, 4, 7, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, let's calculate the squared differences from the mean. $\newline$ $(2 - 5)^2 + (6 - 5)^2 + (7 - 5)^2 + (5 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (4 - 5)^2$ $\newline$ = $(-3)^2 + (1)^2 + (2)^2 + (0)^2 + (-1)^2 + (2)^2 + (-1)^2$ $\newline$ = $9 + 1 + 4 + 0 + 1 + 4 + 1$ $\newline$ = $20$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ Variance $\sigma^2$ = Sum of squared differences / Number of data points $\newline$ Variance $\sigma^2$ = $\frac{20}{7}$ $\newline$ Variance $\sigma^2$ $\approx 2.9$ when rounded to the nearest tenth.