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In the data set below, what is the variance? $\newline$ $1, 2, 2, 7, 6, 9$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $\sigma^2$ : _____

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Variance and standard deviation

Full solution

Q. In the data set below, what is the variance?

\newline

1, 2, 2, 7, 6, 9

\newline

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

\newline

variance

\sigma^2

: _____

Calculate Sum of Squared Differences: Now, calculate the sum of the squared differences from the mean for each data point. $\newline$ $\Sigma(x_i - \mu)^2 = (1 - 4.5)^2 + (2 - 4.5)^2 + (2 - 4.5)^2 + (7 - 4.5)^2 + (6 - 4.5)^2 + (9 - 4.5)^2$ $\newline$ $= (-3.5)^2 + (-2.5)^2 + (-2.5)^2 + (2.5)^2 + (1.5)^2 + (4.5)^2$ $\newline$ $= 12.25 + 6.25 + 6.25 + 6.25 + 2.25 + 20.25$ $\newline$ $= 53.5$
Find Variance: Finally, divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 6$ (number of data points) $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{53.5}{6}$ $\newline$ $\sigma^2 = 8.916666...$ $\newline$ Round the variance to the nearest tenth. $\newline$ $\sigma^2 \approx 8.9$

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