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

6, 1, 2, 2, 3

\newline

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

\newline

variance

\sigma^2

: _____

Calculate Mean: Calculate the mean of the data set. $\newline$ Mean = $(6 + 1 + 2 + 2 + 3)/5$ $\newline$ $\mu = 14/5$ $\newline$ $\mu = 2.8$
Calculate Sum of Squared Deviations: Data set: $6, 1, 2, 2, 3$ $\newline$ $\mu = 2.8$ $\newline$ Calculate the sum of the squared deviations from the mean. $\newline$ $(6 - 2.8)^2 + (1 - 2.8)^2 + (2 - 2.8)^2 + (2 - 2.8)^2 + (3 - 2.8)^2$ $\newline$ = $(3.2)^2 + (-1.8)^2 + (-0.8)^2 + (-0.8)^2 + (0.2)^2$ $\newline$ = $10$ . $24$ + $3$ . $24$ + $0$ . $64$ + $0$ . $64$ + $0$ . $04$ $\newline$ = $14$ . $8$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 14.8$ $\newline$ $N= 5$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 14.8/5$ $\newline$ $\sigma^2 = 2.96$ $\newline$ $\sigma^2 \approx 3.0$

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