Concept explainers
The interquartile range of given data
Answer to Problem 6MCQ
Option A. 13
Explanation of Solution
Given:
The given data is:
45, 57, 55, 42, 48, 21, 39, 62, 45, 51
Calculation:
To find the interquartile range of the given data:
Order the data from least to greatest
21, 39, 42, 45, 45, 48, 51, 55, 57, 62
Now, find the median of the ordered data:
As the number of data items are 10 (even), the median will be 5th data value + 6th data value/2.
So, Median will be:
Now, we will calculate the median of lower data set and the upper data set.
Divide the given data set having 10 data items into two data sets with 5 data items each.
So, lower data set will be:
21, 39, 42, 45, 45
And the upper data set will be:
48, 51, 55, 57, 62
We will calculate the median of both these data sets now.
Median of lower data set:
21, 39, 42, 45, 45
Median will be the exact middle value as the number of terms are 5 (odd).
So, Median of lower data set = 42
Median of upper data set:
48, 51, 55, 57, 62
Median will be the exact middle value as the number of terms are 5 (odd).
So, Median of upper data set = 55
Lastly, subtract the median of lower data set from the median of upper data set to get the Interquartile range.
Median of lower data set = 42
Median of upper data set = 55
Interquartile Range = 55 - 42
Interquartile Range = 13
So, Option A. 13 is the correct answer.
Chapter 13 Solutions
Pre-Algebra, Student Edition
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