For the given data, we will calculate the interquartile before and after Pat's minutes and keenan's minutes are removed from the data
So, the given data in order from least to the greatest will be:
6 , 12 , 16 , 16 , 18 , 20 , 22 , 24
we will divide the data into 2 sections
( 6 , 12 , 16 , 16 ) , ( 18 , 20 , 22 , 24 )
The median of the first section = Q1 = (12 + 16)/2 = 14
The median of the second section = Q3 = ( 20 + 22 )/2 = 21
So, interquartile range = Q3 - Q1 = 21 - 14 = 7
Now, we will calculate the interquartile range when Pat's minutes and keenan's minutes are removed from the data
So, the data will be:
12 , 16 , 16 , 18 , 20 , 22
Divide the data into 2 sections:
( 12 , 16 , 16 ) , ( 18 , 20 , 22 )
The median of the first section will be = Q1 = 16
The median of the second section = Q3 = 20
So, interquartile range = Q3 - Q1 = 20 - 16 = 4
Now, we will compare the results:
the interquartile range before removing = 7
the interquartile range after removing = 4
So, 7 - 4 = 3
This means: the interquartile range is decreased by 3
So, the answer is option b