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In the data set below, what is the variance? $\newline$ $1, 3, 1, 2, 6, 9, 6$ $\newline$ 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, 3, 1, 2, 6, 9, 6

\newline

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

\newline

variance

(\sigma^2)

: _____

Calculate Sum Squared Differences: Now, let's calculate the sum of the squared differences from the mean. $\newline$ $\Sigma(x_i - \text{mean})^2 = (1 - 4)^2 + (3 - 4)^2 + (1 - 4)^2 + (2 - 4)^2 + (6 - 4)^2 + (9 - 4)^2 + (6 - 4)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 9 + 1 + 9 + 4 + 4 + 25 + 4$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 56$
Divide by Number of Data Points: Finally, we divide the sum of squared differences by the number of data points to find the variance. $\newline$ $N = 7$ $\newline$ Variance $\sigma^2$ = $\Sigma(x_i - \text{mean})^2 / N$ $\newline$ Variance $\sigma^2$ = $56 / 7$ $\newline$ Variance $\sigma^2$ = $8$

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