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

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