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In the data set below, what is the variance? $\newline$ $1, 4, 8, 3, 4, 7, 1$ $\newline$ 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, 4, 8, 3, 4, 7, 1

\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. $\newline$ $\Sigma(x_i - \text{mean})^2 = (1 - 4)^2 + (4 - 4)^2 + (8 - 4)^2 + (3 - 4)^2 + (4 - 4)^2 + (7 - 4)^2 + (1 - 4)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = (-3)^2 + (0)^2 + (4)^2 + (-1)^2 + (0)^2 + (3)^2 + (-3)^2$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 9 + 0 + 16 + 1 + 0 + 9 + 9$ $\newline$ $\Sigma(x_i - \text{mean})^2 = 44$
Calculate Variance: Finally, we calculate the variance by dividing the sum of squared differences by the number of data points. $\newline$ Variance $\sigma^2$ = $\frac{\Sigma(x_i - \text{mean})^2}{N}$ $\newline$ Variance $\sigma^2$ = $\frac{44}{7}$ $\newline$ Variance $\sigma^2$ $\approx 6.3$ (rounded to the nearest tenth)

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