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In the data set below, what is the variance? $\newline$ $2, 7, 1, 2, 5, 4$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Variance and standard deviation

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

\newline

2, 7, 1, 2, 5, 4

\newline

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

\newline

variance

(\sigma^2)

: _____

Data Set: Data set: $2, 7, 1, 2, 5, 4$ $\newline$ Mean $\mu = 3.5$ $\newline$ Calculate the sum of the squared deviations from the mean $\Sigma(x_i - \mu)^2$ . $\newline$ $(2 - 3.5)^2 + (7 - 3.5)^2 + (1 - 3.5)^2 + (2 - 3.5)^2 + (5 - 3.5)^2 + (4 - 3.5)^2$ $\newline$ $= (-1.5)^2 + (3.5)^2 + (-2.5)^2 + (-1.5)^2 + (1.5)^2 + (0.5)^2$ $\newline$ $= 2.25 + 12.25 + 6.25 + 2.25 + 2.25 + 0.25$ $\newline$ $= \(25\).\(5\)
Calculate Sum of Squared Deviations: We have:\(\newline\)\(\Sigma(x_i - \mu)^2= 25.5\)\(\newline\)Number of data points \(N= 6\)\(\newline\)Calculate the variance \(\sigma^2\) and round your answer to the nearest tenth.\(\newline\)\(\sigma^2 = (\Sigma(x_i - \mu)^2)/N\)\(\newline\)\(\sigma^2 = 25.5/6\)\(\newline\)\(\sigma^2 = 4.25\)\(\newline\)Since we need to round to the nearest tenth, \(\sigma^2 \approx 4.3\)

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