Nuclear power plants.According to the Nuclear Energy Institute (NEI), 62 nuclear power plants were operating in the United States in 2015. The table at top of the next column lists the 30 states that operate nuclear power

plants, the number of plants in each state, and whether the state has passed legislation supporting nuclear energy expansion (regulated) or not (deregulated).

a.Find the mean, median, and mode of the number of power plants per state. Interpret these values.

b.Repeat part afor the regulated states only.

c.Repeat part afor the deregulated states only.

d.Compare the results, parts band c.What inference can you make about the impact that state regulation has on the number of nuclear power plants?

e.Eliminate the state with the largest number of power plants from the data set and repeat part a.What effect does dropping this measurement have on the measures of central tendency found in part a?

f.Arrange the 30 values in the table from lowest to highest. Next, eliminate the lowest two values and the highest two values from the data set and find the mean of the remaining data values. The result is called a 10% trimmed meanbecause it is calculated after removing the highest 10% and the lowest 10% of the data values. What advantages does a trimmed mean have over the regular arithmetic mean?

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

$$\begin{gathered} Mean=\frac{Sumofallpowerplants}{Numberofstates} \\ =\frac{62}{30} \\ =2.066 \end{gathered}$$

Therefore, the mean is 2.066.

Arranging the number of power plants per state in ascending order,

(1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,5,6)

$$\begin{gathered} Median=\frac{Sumof15thand16thvalue}{2} \\ =\frac{2+2}{2} \\ =\frac{4}{2} \end{gathered}$$

Therefore, the median is 2.

As 1 is repeated maximum times (13) in the data set,1 is the mode.

Therefore, the mean is 1.82.

$$\begin{gathered} Mean=\frac{Sumofallpowerplantsinregulatedstates}{Noofregulatedstate} \\ =\frac{2+1+1+1+3+2+1+2+23+1+1+2+3+4+2+2+1}{17} \\ =\frac{31}{17} \\ =1.82 \end{gathered}$$

Organizing the number of power plants in regulated states in ascending order,

(1,1,1,1,1,1,1, 2,2,2,2,2,2,2,3,3,4)

As the number of plants is 17, the median is 2.

Here we have 2 modes. Because 1 and 2 are both repeated 7 times and 7 is the highest count.

Therefore, the 2 modes are 1 and 2.

$$\begin{gathered} Mean=\frac{Sumofallpowerplantsinregulatedstates}{Noofregulatedstate} \\ =\frac{1+6+1+1+1+3}{13} \\ =\frac{31}{13} \\ =2.38 \end{gathered}$$

Therefore, the mean is 2.38.

To find the median, we will first note down the values in ascending order.

(1,1,1,1,1,1,2,2,3,3,4,5,6)

2 is the midpoint of the list of values.

Therefore, the median is 2.

The highly repeated value is 1. Therefore, the model is 1.

While the median and the mode are the same for both states, the average number of power plants per state is higher in the deregulated states because of the few states who have a very high number of power plants.

The highest number of power plants (6) is in Illinois. Therefore, we will remove this value from consideration.

$$\begin{gathered} Mean=\frac{Sumofallpowerplants}{Noofstates} \\ =\frac{56}{20} \\ =1.93 \end{gathered}$$

Therefore, the new mean is 1.93.

Writing down the values in ascending order,

(1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3,3,4,4,5)

Mid-point of the values is the 15^th value. Therefore, the median is 2.

1 is repeated maximum times, and 1 is the mode.

When the largest value is removed from the data set, the mean value becomes smaller

Arranging the table in ascending order and eliminating the highest and lowest two values we get,

$$\begin{gathered} Trimmedmean=\frac{Sumofallpowerplants}{Noofstates} \\ =\frac{49}{26} \\ =1.88 \end{gathered}$$

Therefore, the trimmed mean value is 1.88.

A trimmed mean is a better measure than a regular mean because it is not influenced by the outlier values. Sometimes the values on the tails of the distribution affect the regular mean and pull the mean towards the tail. To avoid the impact of a few outliers, a trimmed mean is used