Question

the weekly salaries of a sample of employees at the local bank are given in the table below.

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$$\begin{tabular}{|c|c|} \\hline employee & weekly salary \\\\ \\hline anja & \\$245 \\\\ \\hline raz & \\$300 \\\\ \\hline natalie & \\$325 \\\\ \\hline mic & \\$465 \\\\ \\hline paul & \\$100 \\\\ \\hline \\end{tabular}$$

what is the variance for the data?

variance: \\(s^2 = \frac{(x_1 - \bar{x})^2 + (x_2 - \bar{x})^2 + \dots + (x_n - \bar{x})^2}{n - 1}\\)

\\(\bigcirc\\) 118.35
\\(\bigcirc\\) 132.32

Explanation:

Calculate the sample mean

Using the Sample Variance Formula knowledge point

$$ \bar{x} = \frac{245 + 300 + 325 + 465 + 100}{5} = \frac{1435}{5} = 287 $$

Compute squared deviations

Using the Sample Variance Formula knowledge point

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Sum the squared deviations

Using the Sample Variance Formula knowledge point

$$ \sum (x_i - \bar{x})^2 = 1764 + 169 + 1444 + 31684 + 34969 = 70030 $$

Calculate the sample variance

Using the Sample Variance Formula knowledge point

$$ s^2 = \frac{70030}{5 - 1} = \frac{70030}{4} = 17507.5 $$

Answer:

• (A) 118.35
• (B) 132.32
• (C) 17507.5 (Correct answer)
• (D) 14006