Using the given sample data, calculate the following measures of dispersion, to one decimal place.

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asked Jan 1, 2023 136k views

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Volox · Answer 1 · 2023-01-07T20:27:04+0000

Answer:

Range = 15

Variance = 24.5Explanations

Standard deviation = 5.0

The formula for calculating the range is expressed as:

Range = Highest value - Lowest value

Range = 24 - 9

Range = 15

Calculate the variance

The formula for calculating the variance is expressed as:

$Variance=\frac{\sum(x-\overline{x})^2}{n-1}$

Find the mean

$\begin{gathered} mean=(9+13+15+18+19+20+24)/(7) \\ mean\text{ }\overline{x}=(118)/(7)=16.9 \end{gathered}$

Determine the variance

$\begin{gathered} S^2=((9-16.9)^2+(13-16.9)^2+(15-16.9)^2+(18-16.9)^2+(19-16.9)^2+(20-16.9)^2+(24-16.9)^2)/(7-1) \\ S^2=(146.9)/(6) \\ S^2\approx24.5 \end{gathered}$

Determine the standard deviation

$\begin{gathered} S=√(variance) \\ S=√(24.5) \\ S\approx5.0 \end{gathered}$

Using the given sample data, calculate the following measures of dispersion, to one decimal place.

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