Make box-and-whisker plots to compare the data sets
Test scores;
Andrew’s: 79 80 87 87 99 94 77 86
Dipak s: 93 79 78 82 91 87 80 99
Draw the box-and-whisker plots to compare the given data sets.
Answer to Problem 18P
Explanation of Solution
Given:
Test scores:
A’s : 79 , 80 , 87 , 87 , 99 , 94 , 77 , 86
D’s : 93 , 79 , 78 , 82 , 91 , 87 , 80 , 99
Calculation: ,
A’s test scores:
Arrange the data in ascending order:
77 , 79 , 80 , 86 , 87 , 87 , 94 , 99
The minimum is 77.
The first quartile is the median of the lower half of the data set.
Since the total entries are 8, which is even , So, the lower half is the first
So , the first quartile is
Median = The mean of
The third quartile is the median of the upper half of the data set.
Since the total entries are 8, which is even , So, the upper half is the last
So , the third quartile is
The maximum is 99.
D’s test scores:
Arrange the data in ascending order:
78 , 79 , 80 , 82 , 87 , 91 , 93 , 99
The minimum is 78.
The first quartile is the median of the lower half of the data set.
Since the total entries are 8, which is even , So, the lower half is the first
So , the first quartile is
Median = The mean of
The third quartile is the median of the upper half of the data set.
Since the total entries are 8, which is even , So, the upper half is the last
So , the third quartile is
The maximum is 99.
Represent the above details on the number line. Draw the box through the first and third quartile and make a vertical line through the median , and whisker from the minimum to the maximum data entry.
Since the box of D’s test score is longer than that of A’s test score . So, D has more interquartile range.That is the median of D’s test score varies more widely than the median or middle test score of A.
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