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Data With Outliers
Lesson 3-2
Pg. # 91-93
CA Content Standards
Statistics, Data Analysis, and Probability 1.3:
I understand how leaving out or including outliers
affects measures of central tendency.
Statistics, Data Analysis, and Probability 1.2:
I understand how additional data may affect
computations of central tendency.
Mathematical Reasoning 2.2:
I apply strategies from simpler problems to more difficult
problems.
Review Vocabulary:
MEASURES OF CENTRAL
TENDENCY
 Measuring tools (such as mean, median,
and mode) that indicate what is typical, or
common, in a set of data.
Vocabulary:
OUTLIER
 An extreme value in a data set, separated
from most of the other values.
Objective
Compute the mean, median, mode, and
range of data sets with and without outliers
to determine how they affect central
tendencies.
Math Link: You know how to find the mean,
median, and mode of a data set. Now you
will learn how one unusual number in a set
of data can affect these measures of
central tendency.
Example 1.
 Miss Flores asked some of her 6th grade math students
how many hours of television they watch daily.
Hours of Television Viewed (Daily)
Name
Total No. of Hours
Sam
1
Dominik
2
Brianna
1
Paul
1
Mario
3
Erica
1
Maria
2
 Use the data in the table to calculate mean, median, and
mode. These calculations will let us know how many
hours are most typical per person.
 Mean:
1 + 2 + 1 + 1 + 3 + 1 + 2 = 11 = 1.6
7
7
 Median:
1
1
1
1
2
2
3
 Mode:
The number 1 appears the most times. 1 is the mode.
According to our calculations, most participants watch
approximately 1 hour of television every day.
***Note: Even though we have a mean of 1.6, no participant
watched exactly 1 and six-tenths of an hour of TV. This is
an example of how a mean can describe the group but not
any individual member of the group.
Example 2.
Hannah is not listed in the table. She
watches 9 hours every day. (Talk about a
COUCH POTATO!) Add Hannah’s data to
the data set and recalculate the mean,
median, and mode. Are the mean, median,
and mode affected by this extra data?
 Mean:
1 + 2 + 1 + 1 + 3 + 1 + 2 + 9 = 20 = 2.5
8
8
 Median:
1
1
1
1
2
2
3
9
Median = 1.5
 Mode:
The number 1 appears the most times. 1 is the mode.
According to our calculations, most participants watch between 1 and 2.5
of television every day.
Did our mean change when we added Hannah’s information? How about
the median? The mode?
Would the median or mode change if Hannah watched 4 hours daily? 12
hours?
Hannah’s data is an outlier. An outlier is a
number in a data set that is very different
from the rest of the numbers. Outliers can
have a great effect on the mean.
Outliers usually do not impact the median
or mode.
Data sets can have more than one outlier.
Example 3.
 Throughout most of the year, Acapulco is very
sunny. If you look at the # of wet days from
February through May, you see the range is from
0 to 2. But when the rainy season begins in June,
the number of wet days jumps to 12. 12 is an
outlier in this set of data because it is very
different from the rest of the numbers.
Number of wet days in
Acapulco, Mexico
February
1
March
0
April
0
May
2
June
12
Mean
Feb - May
Feb - June
1+0+0+2=3
3 ÷ 4 = 0.75
Mean = 0.75
1 + 0 + 0 + 2 + 12 = 15
15 ÷ 5 = 3
Mean = 3
Median
0 0 1 2
Median = 0.5
0
0 1 2 12
Median = 1
Mode
0
0
0 1 2
Mode = 0
0 1 2
Mode = 0
12
The outlier did not affect the mode, and it changed the median slightly. But
look what happens to the mean when the June number is included in the
data. The mean becomes 3 wet days, which is the same as Feb through
May combined.
Identify the outlier. Then find the mean, median, and mode of the data with
and without the outlier.
190
Mean
210
160
250
1400
190
With Outlier
Without Outlier
190+210+160+250+1400+
190 = 2400
190+210+160+250+190= 1000
2400 ÷ 6 = 400
Mean = 400
1000 ÷ 5 = 200
Mean = 200
Median = 200
Median = 190
Mode = 190
Mode = 190
Median
Mode
The Moral of the Story:
An outlier is a value within a set of data
that is far below or far above most of the
other data. It can affect the median, but
usually has the greatest effect on the
mean of a set of data.