In the data set below, what is the variance? 6, 9, 7, 1, 9, 4 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Squared Differences: Now, calculate the squared differences from the mean for each data point. (6 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (1 - 6)^2 + (9 - 6)^2 + (4 - 6)^2 = 0^2 + 3^2 + 1^2 + (-5)^2 + 3^2 + (-2)^2 = 0 + 9 + 1 + 25 + 9 + 4 = 48Find Variance: Next, divide the sum of squared differences by the number of data points to find the variance. N = 6 σ^2 = Σ(x_i - μ)^2 / N σ^2 = 48 / 6 σ^2 = 8Final Result: Since the variance is a whole number, there is no need to round to the nearest tenth. The variance of the data set is 8.

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In the data set below, what is the variance? $\newline$ $6, 9, 7, 1, 9, 4$ $\newline$ 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

6, 9, 7, 1, 9, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Squared Differences: Now, calculate the squared differences from the mean for each data point. $\newline$ $(6 - 6)^2 + (9 - 6)^2 + (7 - 6)^2 + (1 - 6)^2 + (9 - 6)^2 + (4 - 6)^2$ $\newline$ $= 0^2 + 3^2 + 1^2 + (-5)^2 + 3^2 + (-2)^2$ $\newline$ $= 0 + 9 + 1 + 25 + 9 + 4$ $\newline$ $= 48$
Find Variance: Next, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 6$ $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{48}{6}$ $\newline$ $\sigma^2 = 8$
Final Result: Since the variance is a whole number, there is no need to round to the nearest tenth. $\newline$ The variance of the data set is $8$ .