Question

Data set X and data set Y both have the same interquartile range. If the first quartile of data set X is less than the first quartile of data set Y, then the third quartile of data set X is greater than the third quartile of data set Y.
a. true
b. false

Answer 1

well the distance between the quartiles Q1 to Q3 is the same...

lets say the interquartile range is 10 for both X and Y

so in set X: if Q1 = 5 then Q3 = 15

in set Y : if Q1 = 15 then Q3 = 25

so the distance between the Q1 in set X and Q1 in Set Y will be the same for the upper quartiles Q3

hope it helps

Answer 2

in the example I used both set X and Y have IQR = 10... the distance between the Q! values was 10, the the Q3 values need the same distance