In the data set below, what is the variance? 8, 7, 9, 6, 2, 1, 2 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Sum of Squared Differences: Now we got the mean, let's calculate the sum of the squared differences from the mean. (8 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (6 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (2 - 5)^2 = 3^2 + 2^2 + 4^2 + 1^2 + (-3)^2 + (-4)^2 + (-3)^2 = 9 + 4 + 16 + 1 + 9 + 16 + 9 = 64Find Variance: Alright, we have the sum of the squared differences. Now, let's divide by the number of data points to find the variance. Variance (σ^2) = Sum of squared differences / Number of data points Variance (σ^2) = 64 / 7 Variance (σ^2) ≈ 9.1 (rounded to the nearest tenth)

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In the data set below, what is the variance? $\newline$ $8, 7, 9, 6, 2, 1, 2$ $\newline$ 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

8, 7, 9, 6, 2, 1, 2

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum of Squared Differences: Now we got the mean, let's calculate the sum of the squared differences from the mean. $\newline$ $(8 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (6 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (2 - 5)^2$ $\newline$ = $3^2 + 2^2 + 4^2 + 1^2 + (-3)^2 + (-4)^2 + (-3)^2$ $\newline$ = $9 + 4 + 16 + 1 + 9 + 16 + 9$ $\newline$ = $64$
Find Variance: Alright, we have the sum of the squared differences. Now, let's divide by the number of data points to find the variance. $\newline$ Variance $\sigma^2$ = Sum of squared differences / Number of data points $\newline$ Variance $\sigma^2$ = $\frac{64}{7}$ $\newline$ Variance $\sigma^2$ $\approx 9.1$ (rounded to the nearest tenth)