Select the true statements. The interquartile range of A is 1 less than the interquartile range of B.
Including the runs allowed in the tenth game does not cause the spread of the data to change
The median of A is the same as the median of B.
The interquartile range of B is greater than the interquartile range of A.
The median of B is 1 run more than the median of A.
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The true statements are;

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

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

Explanation:

The given parameters are;

The set of the number of runs, A = {1, 4, 2, 2, 3, 1, 1, 2, 1}

The number of runs the pitcher allows in the tenth game = 9 runs

The set of the number of runs allowed in 10 games B = {1, 4, 2, 2, 3, 1, 1, 2, 1, 9}

Rearranging the data, we get  

A = 1, 1, 1, 1, 2, 2, 2, 3, 4

B = 1, 1, 1, 1, 2, 2, 2, 3, 4, 9

For the set A, we have;

Q₁ = 1, Q₂ = 2, Q₃ = 2

Therefore, the interquartile range of A = Q₃ - Q₁ = 2.5 - 1 = 1.5

For the set B, we have;

Q₁ = 1, Q₂ = 2, Q₃ = 2

Therefore, the interquartile range of A = Q₃ - Q₁ = 3.25 - 1 = 2.25

Therefore, the correct answers with regards to the two data are;

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

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