Question

1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
26 31 40 28 19 23 35 38 43 46 28 30
(a) What is the five-number summary of the data set?
(b) What is the range of the data set? Show your work.
highest number 46 minus lowest number 19 equals 27 range
(c) What is the interquartile range (IQR) of the data set? Show your work.

Answer 1

put the numbers in order
19,23,26,28,28,30,31,35,38,40,43,46

minimum = 19
maximum = 46
Q1 =(26 + 28)/2 = 54/2 = 27
Q2 (median) = (30 + 31)/2 = 61/2 = 30.5
Q3 = (38 + 40)/2 = 78/2 = 39

range = max - min = 46 - 19 = 27

Interquartile Range (IQR) = Q3 - Q1 = 39 - 27 = 12