Question

The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the club. 3 21 10 18 12 3 10 13 12 17 7 3 7 17 14 a. Compute the values of the three quartiles and the interquartile range. Q1= 25 Q2= 33 Q3= 55 IQR= 22 b. Calculate the approximate value of the 82nd percentile. Enter an exact value. c. Find the percentile rank of 12. Round your answer to the nearest integer. %

Answer 1

First arrange the data in an order
3, 3, 3, 7, 7, 10, 10, 12, 12, 13, 14, 17, 17, 18, 21

a.) Q1 = (N + 1)/4th item = (15 + 1)/4 = 4th item = 7
Q2 = 2(16)/4 = 16/2 = 8th item = 12
Q3 = 3(16)/4 = 3(4) = 12th item = 17
IQR = (Q3 - Q1)/2 = (17 - 7)/2 = 10/2 = 5

b.) 82nd percentile = 82(16)/100 = 13th item = 17

c.) 12 is the 8th item which is in the middle of the data set, so the percentile rank is 50%