Select ALL the correct answers. A pitcher for a professional baseball team allows runs in the first nine games he starts this season. Let A be the set of the number of

runs allowed by the pitcher in his first nine starts.

A = {1, 4, 2, 2, 3, 1, 1, 2, 1}

In the tenth game he starts, he allows 9 runs. Let B represent the set of the number of runs allowed in all ten games he has started.

Select the true statements.

The median of B is 1 run more than the median of A.

The interquartile range of B is greater than the interquartile range of A.

The interquartile range of A is 1 less than the interquartile range of B.

The median of A is the same as the median of B.

Including the runs allowed in the tenth game does not cause the spread of the data to

change.

(b) The interquartile range of B is greater than the interquartile range of A.

(d) The median of A is the same as the median of B.

Explanation:

Given

So:

Required

Select all true statements

(a) & (d) Median Comparisons

Arrange the data:

                                --- average of 5th and 6th

Option (d) is correct because both have a median of: 2

(b) & (c) Interquartile Range Comparisons

First, calculate the lower quartile (Q1)

[Odd n]             [Even n]

This means that:

Next, calculate the upper quartile (Q3)

[Odd n]             [Even n]

This means that:

The interquartile range is  

So, we have:

(b) is true because B has a greater IQR than A

(e) This is false because some spread measures (which include quartiles and the interquartile range) changed when the 10th data is included.

The upper quartile and the interquartile range of A and B are not equal

a and c are the answeres