Active nuclear power plants.Refer to Exercise 2.54 (p. 98) and the Nuclear Energy Institute’s data on the number of nuclear power plants operating in each of 30 states.

a.Find the range, variance, and standard deviation of this data set.

b.Eliminate the largest value from the data set and repeat part a.What effect does dropping this measurement have on the measures of variation found in part a?

c.Eliminate the smallest and largest value from the data set and repeat part a. What effect does dropping both of these measurements have on the measures of variation found in part a?

State	Status	Number of Power Plants
Alabama	Regulated	2
Arizona	Regulated	1
Arkansas	Regulated	1
California	Regulated	1
Connecticut	Deregulated	1
Florida	Regulated	3
Georgia	Regulated	2
Illinois	Deregulated	6
Iowa	Deregulated	1
Kansas	Regulated	1
Louisiana	Regulated	2
Maryland	Deregulated	1
Massachusetts	Deregulated	1
Michigan	Deregulated	3
Minnesota	Regulated	2
Mississippi	Regulated	1
Missouri	Regulated	1
Nebraska	Regulated	2
New Hampshire	Deregulated	1
New Jersey	Deregulated	3
New York	Deregulated	4
North Carolina	Regulated	3
Ohio	Deregulated	2
Pennsylvania	Deregulated	5
South Carolina	Regulated	4
Tennessee	Regulated	2
Texas	Deregulated	2
Virginia	Regulated	2
Washington	Regulated	1
Wisconsin	Deregulated	1

Step by step solution

01

Finding the range, variance, and standard deviation

$\begin{array}{rcl}\mathrm{Range}& =& \mathrm{Max}-\mathrm{Min}\\ & =& 6-1\\ & =& 5\end{array}$

$\begin{array}{rcl}\mathrm{Mean}& =& \frac{\mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{powerplants}}{\mathrm{No}.\mathrm{of}\mathrm{states}}\\ & =& \frac{2+1+1+1+1+3+2+6+1+1+2+1+1+3+2+1+1+2+1+3+4+3+2+5+4+2+2+2+1+1}{30}\\ & =& \frac{62}{30}\\ & =& 2.066\\ & & \end{array}$

$\begin{array}{rcl}Variance& =& \frac{\sum {\left(x-\overline{x}\right)}^2}{n-1}\\ & =& \frac{49.86668}{29}\\ & =& 1.72\end{array}$

$\begin{array}{rcl}S\tan dardDeviation& =& \sqrt{Variance}\\ & =& \sqrt{1.72}\\ & =& 1.31\end{array}$

02

Removing the largest and the smallest value and repeating Step 1

$\begin{array}{rcl}Range& =& Max-Min\\ & =& 5-1\\ & =& 4\end{array}$

$\begin{array}{rcl}Mean& =& \frac{Sumofallpowerplants}{No.ofstates}\\ & =& \frac{2+1+1+1+1+3+2+1+1+2+1+1+3+2+1+1+2+1+3+4+3+2+5+4+2+2+2+1+1}{29}\\ & =& \frac{56}{29}\\ & =& 1.93\end{array}$

$\begin{array}{rcl}\mathrm{Variance}& =& \frac{\sum {\left(\mathrm{x}-\overline{\mathrm{x}}\right)}^2}{\mathrm{n}-1}\\ & =& \frac{34.39}{28}\\ & =& 1.21\end{array}$

$\begin{array}{rcl}S\tan darddeviation& =& \sqrt{Variance}\\ & =& \sqrt{1.21}\\ & =& 1.1\end{array}$

When the largest value is removed, the variance and the standard deviation decrease. This indicates the impact of outliers on the distribution.

03

Removing the largest value and repeating Step 1

$\begin{array}{rcl}Range& =& Max-Min\\ & =& 5-1\\ & =& 4\end{array}$

$\begin{array}{rcl}Mean& =& \frac{Sumofallpowerplants}{No.ofstates}\\ & =& \frac{55}{28}\\ & =& 1.96\\ & & \end{array}$

$\begin{array}{rcl}Variance& =& \frac{\sum \left(x-\overline{x}\right)}{n-1}\\ & =& \frac{32.96}{27}\\ & =& 1.22\end{array}$

$\begin{array}{rcl}S\tan dardDeviation& =& \sqrt{Variance}\\ & =& \sqrt{1.22}\\ & =& 1.1\end{array}$

When the largest and the smallest values are removed from the data, the variance and the standard deviation reduce.

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