Range and Outliers

MFT
TP
O
Range and Outliers
CA Standards
SDAP 1.1
SDAP 1.3
Goal: Analyze how the inclusion or exclusion of outliers affects measures of
central tendency.
Vocabulary
Lower extreme:
The least data value in a data set
Upper extreme: The greatest data value in a data set
Lower quartile: The median of the lower half of the data
Upper quartile: The median of the upper half of the data
Range:
The difference between the upper and lower extremes of
a data set
Interquartile range: The difference between the upper and lower
quartiles
Outlier:
A value in a data set that is much greater or much less
than the other values
Box-and-whisker plot:
A data display that divides data values into
four parts
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Lesson 7.4 • Course 1 Notetaking Guide
153
EXAMPLE
1
Computing Statistics
Find the median, extremes, quartiles, range, and interquartile range of
the data set 22, 36, 24, 40, 18, 56, 33, 87, and 25.
Step 1 Order the data and identify the median and the extremes.
18
22
24
25
Lower
extreme
40
56
87
Upper
extreme
Step 2 Identify the quartiles using the lower and upper halves of the
data.
18
22
24
25
36
Lower quartile
40
56
If a data set has an
odd number of values,
the median is not
included in either the
lower half or upper half.
36
Median
WATCH OUT!
33
87
Upper quartile
22 24 2 23
40 56 2 48
Step 3 Subtract the extremes to find the range:
87 18 69 .
Step 4 Subtract the quartiles to find the interquartile:
range: 48 23 25 .
EXAMPLE
2
Describing Effects of Outliers
Use the data set 59, 60, 64, 66, 68, 72, and 115. The data value 115 is
an outlier. How does the exclusion of the outlier affect the mean? Explain.
Solution
Calculate the mean of the original data set.
Mean:
504 72
}
59 + 60 + 64 + 66 + 68 + 72 + 115
}}}
7
7
Then calculate the mean excluding the outlier 115 .
Mean:
59 + 60 + 64 + 66 + 68 + 72
6
}}}
389 64.8
}
6
The mean decreases by about 7.2 . The mean decreases because the
outlier is the greatest data value .
154
Lesson 7.4 • Course 1 Notetaking Guide
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Guided Practice
Use the data set 14, 12, 18, 15, 13, and 4.
1. Find the median, extremes, quartiles, range, interquartile range, and any
outliers of the data set.
Median: 13.5; lower extreme: 4, upper extreme: 18;
lower quartile: 12; upper quartile: 15; range: 14;
interquartile range: 3; outlier: 4
3
EXAMPLE
Using a Box-and-Whisker Plot
Test Scores The box-and-whisker plots below show the spread of the
differences between the prices of winter coats at 25 stores in a mall. The
data in the first plot have an outlier of $29. The second plot displays the
same data but does not include the outlier. How does excluding the outlier
affect the median and the range of the data?
20
30
29
Lower
extreme
40
50
60
80
90 100
66 75
87 95
Median
Lower
Upper
Upper
quartile
quartile extreme
56
Lower
extreme
Homework
70
68 75
87
95
Upper
Lower Median Upper extreme
quartile
quartile
Solution
When the outlier is included , the median is 75 and the range is 66 .
When the outlier is excluded , the median is 75 and the range is 39 .
The median does not change and the range greatly decreases
when the outlier is excluded.
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Lesson 7.4 • Course 1 Notetaking Guide
155