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In the data set below, what is the variance? $\newline$ $5, 3, 2, 9, 2, 4, 3$ $\newline$ 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

5, 3, 2, 9, 2, 4, 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 = $(5 + 3 + 2 + 9 + 2 + 4 + 3)/7$ $\newline$ $\mu = 28/7$ $\newline$ $\mu = 4$
Calculate Squared Differences: Data set: $5, 3, 2, 9, 2, 4, 3$ $\newline$ $\mu = 4$ $\newline$ Calculate the sum of the squared differences from the mean. $\newline$ $(5 - 4)^2 + (3 - 4)^2 + (2 - 4)^2 + (9 - 4)^2 + (2 - 4)^2 + (4 - 4)^2 + (3 - 4)^2$ $\newline$ $= (1)^2 + (-1)^2 + (-2)^2 + (5)^2 + (-2)^2 + (0)^2 + (-1)^2$ $\newline$ $= 1 + 1 + 4 + 25 + 4 + 0 + 1$ $\newline$ $= 36$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 36$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = (\Sigma(x_i - \mu)^2)/N$ $\newline$ $\sigma^2 = 36/7$ $\newline$ $\sigma^2 \approx 5.1$ when rounded to the nearest tenth.

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