Question

{Exercise 3.19 (Algorithmic)}
The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A lower index value means better or cleaner air. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.

1. Compute the range and interquartile range.

interquartile range: _____________

Answer 1

Given 9 data values in ascending order as follows :

28, 42, 45, 48, 49, 50, 55, 58, 60

a) Minimum value = 28 and Maximum value = 60

=> Range = Maximum - Minimum = 60 - 28 = 32

=> Range = 32

Median = (n + 1)/2 = (9 + 1)/2 = 10/2 = 5th value

=> Median = 49

Q1 = middle value of lower half of median = 3rd value

=> Q1 = 45

Q3 = middle value of upper half of median = 8th value

=> Q3 = 55

IQR = Q3 - Q1 = 55 - 45 = 10

Therefore, range = 32 and Interquartile range = 10