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In the data set below, what is the variance? $\newline$ $3, 6, 4, 7, 9, 3, 3$ $\newline$ 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

3, 6, 4, 7, 9, 3, 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 = $(3 + 6 + 4 + 7 + 9 + 3 + 3)/7$ $\newline$ $\mu = 35/7$ $\newline$ $\mu = 5$
Calculate Squared Differences: Data set: $3, 6, 4, 7, 9, 3, 3$
$\mu = 5$
Calculate the sum of the squared differences from the mean, $\Sigma(x_i - \mu)^2$ .
$(3 - 5)^2 + (6 - 5)^2 + (4 - 5)^2 + (7 - 5)^2 + (9 - 5)^2 + (3 - 5)^2 + (3 - 5)^2$
$= (-2)^2 + (1)^2 + (-1)^2 + (2)^2 + (4)^2 + (-2)^2 + (-2)^2$
$= 4 + 1 + 1 + 4 + 16 + 4 + 4$
$= 34$
Calculate Variance: We know: $\newline$ $\Sigma(x_i - \mu)^2= 34$ $\newline$ $N= 7$ $\newline$ Calculate the variance and round your answer to the nearest tenth. $\newline$ $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ $\newline$ $\sigma^2 = \frac{34}{7}$ $\newline$ $\sigma^2 \approx 4.857$ $\newline$ Round to the nearest tenth: $\sigma^2 \approx 4.9$

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