Question

Question 13

A​ country's Energy Information Administration monitors all nuclear power plants operating in that country. The table below lists the number of active nuclear power plants operating in each of a sample of 10 states.

State	Number of Power Plants
1	5
2	5
3	9
4	8
5	4
6	4
7	2
8	3
9	13
10	3

Eliminate the smallest value from the data set. Then, find the​ variance of this data set. (Round to three decimal places as​ needed.)

Question 14

A​ country's Energy Information Administration monitors all nuclear power plants operating in that country. The table below lists the number of active nuclear power plants operating in each of a sample of 10 states.

State	Number of Power Plants
1	5
2	5
3	9
4	8
5	4
6	4
7	2
8	3
9	13
10	3

Eliminate the smallest value from the data set. Then, find the​ standard deviation of this data set. (Round to three decimal places as​ needed.)

Question 15

A​ country's Energy Information Administration monitors all nuclear power plants operating in that country. The table below lists the number of active nuclear power plants operating in each of a sample of 10 states.

State	Number of Power Plants
1	5
2	5
3	9
4	8
5	4
6	4
7	2
8	3
9	13
10	3

What effect does eliminating the smallest value from the data set have on the variance and standard deviation?

a.)It decreases the variance and standard deviation.

b.)There is no effect on the variance and standard deviation.

c.)It increases the variance and standard deviation.

Answer 1

Formula for variance & standard deviation is -

a) -

First, we calculate variance for given data -

Observation table -

x	(x-x_bar)^2
5	0.36
5	0.36
9	11.56
8	5.76
4	2.56
4	2.56
2	12.96
3	6.76
13	54.76
3	6.76
56	104.4

Calculation -

Now, we calculate variance of data by eliminating smallest value in data. Here, 2 is the smallest value in data, so we eliminate 2 from the data.

Observation table -

x	(x-x_bar)^2
5	1
5	1
9	9
8	4
4	4
4	4
3	9
13	49
3	9
54	90

Calulations -

Variance of the data after eliminating smallest value (2) from the data is 10.

b) -

First, we calculate standard deviation for given data -

Calculation -

Now, we calculate standard deviation of data by eliminating smallest value in data. Here, 2 is the smallest value in data, so we eliminate 2 from the data.

Calulations -

Variance of the data after eliminating smallest value (2) from the data is 3.162.

c) -

Effect of eliminating smallest value from data on variance & standard deviation -

It decreases variance & standard deviation.

Option A is correct.