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In the data set below, what is the variance? $\newline$ $2, 4, 5, 2, 9, 8$ $\newline$ 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

2, 4, 5, 2, 9, 8

\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 = $(2 + 4 + 5 + 2 + 9 + 8)/6$ $\newline$ $\mu = 30/6$ $\newline$ $\mu = 5$
Calculate Sum of Squared Deviations: Data set: $2, 4, 5, 2, 9, 8$ $\newline$ $\mu = 5$ $\newline$ Calculate the sum of squared deviations from the mean $\Sigma(x_i - \mu)^2$ . $\newline$ $(2 - 5)^2 + (4 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (9 - 5)^2 + (8 - 5)^2$ $\newline$ $= (-3)^2 + (-1)^2 + (0)^2 + (-3)^2 + (4)^2 + (3)^2$ $\newline$ $= 9 + 1 + 0 + 9 + 16 + 9$ $\newline$ $= \(44\)
Calculate Variance: We have:\(\newline\)\(\Sigma(x_i - \mu)^2= 44\)\(\newline\)\(N= 6\)\(\newline\)Calculate the variance and round your answer to the nearest tenth.\(\newline\)\(\sigma^2 = (\Sigma(x_i - \mu)^2)/N\)\(\newline\)\(\sigma^2 = 44/6\)\(\newline\)\(\sigma^2 \approx 7.333...\)\(\newline\)Rounded to the nearest tenth: \(\sigma^2 \approx 7.3\)

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