CLASSWORK 1.9
NAME:
PERIOD:
EXAMINING THE EFFECT OF OUTLIERS
In this worksheet you will be investigating how an outlier affects the mean and median of
a set of data. By the end of the lesson you will be able to explain which measure of
central tendency most accurately represents a set of data with an outlier.
DATA SET 1: Rushing Yards Gained by San Diego Chargers Football Players
The table below show the rushing yards gained by San Diego Chargers Football Players
during the 2006 season.
Player
LaDainian Tomlinson
Michael Turner
Lorenzo Neal
Philip Rivers
Andrew Pinnock
Erick Parker
Vincent Jackson
Charlie Whitehurst
Keenan McCardell
Brandon Manumaleuna
Billy Volek
Mike Scifres


Rushing Yards
1815
502
140
49
25
19
16
13
8
1
-3
-7
Which player is an outlier in the data?
How many rushing yards did he have?
CALCULATIONS:
Calculate the mean and median for the rushing yards, but DO NOT include the outlier in
your calculations. Show your work below.
Mean
Mean =
Median
Median =
CLASSWORK 1.9
NAME:
PERIOD:
Now, recalculate the mean and median for the rushing yards, but this time INCLUDE the
outlier in your calculations. Show your work below.
Mean
Mean =
Median
Median =
SUPPORTING QUESTIONS:
Answer all supporting questions in complete sentences and justify your answers by
referring back to your calculations.
1) Look at your calculations for the mean and median when you DID NOT include the outlier.
 How many players had a rushing total that was less than the mean?
 How many players had a rushing total that was greater than the mean?
 How many players had a rushing total that was less than the median?
 How many players had a rushing total that was greater than the median?
2) Look at your calculations for the mean and median when you DID include the outlier.
 How many players had a rushing total that was less than the mean?
 How many players had a rushing total that was greater than the mean?
 How many players had a rushing total that was less than the median?
 How many players had a rushing total that was greater than the median?
3) Look at your answers for questions #1 and #2. If you wanted to accurately represent the
number of yards that a TYPICAL San Diego Charger gained rushing, should you use the
mean or the median to report the data? Justify your answer with supporting details.
CLASSWORK 1.9
NAME:
PERIOD:
DATA SET 2: Populations of the 10 Largest Cities in Maryland
The table below shows the populations of the 10 largest cities in Maryland
City
Baltimore
Columbia
Silver Spring
Dundalk
Wheaton-Glenmont
Ellicott City
Germantown
Bethesda
Frederick
Gaithersburg


Population
651,154
88,254
76,540
62,306
57,694
56,397
55,419
55,277
52,816
52,455
Which city is an outlier in the data?
What is the population?
CALCULATIONS:
Calculate the mean and median for the populations, but DO NOT include the outlier in
your calculations. Show your work below.
Mean
Mean =
Median
Median =
Now, recalculate the mean and median for the populations, but this time INCLUDE the
outlier in your calculations. Show your work below.
Mean
Mean =
CLASSWORK 1.9
NAME:
PERIOD:
Median
Median =
Finally, calculate how the outlier affected your mean and median. Calculate the
difference between the second calculations and the first calculations.
Mean (Mean with outlier – Mean without outlier)
Difference Between Mean Populations =
Median (Median with outlier – Median without outlier)
Difference Between Median Populations =
SUPPORTING QUESTIONS:
Answer all supporting questions in complete sentences and justify your answers by
referring back to your calculations.
1) Look at your calculations for the difference between the two mean populations. Did the
outlier have a significant effect on the value of the mean population? If so, what was the
effect?
2) Look at your calculations for the difference between the two median populations. Did the
outlier have a significant effect on the value of the median population? If so, what was the
effect?
3) Look at your answers for questions #1 and #2. Summarize how an outlier affects the
mean and median of a set of data.
CLASSWORK 1.9
NAME:
PERIOD:
DATA SET 3: Gross Domestic Product (GDP) of the 10 wealthiest countries


Record the name of each country and the GDP
Report the GDP in billions. For example (United States),
$11,667,515,000,000.00 would be 11,667 billion dollars. For another example
(Spain), $991,442,000,000.00 would be 991 billion dollars
Country


GDP (in billions of
dollars
Which country is an outlier in the data?
What is the GDP of that country?
CALCULATIONS:
Calculate the mean and median for the GDP, but DO NOT include the outlier in your
calculations. Show your work below.
Mean
Mean =
Median
Median =
CLASSWORK 1.9
NAME:
PERIOD:
Now, recalculate the mean and median for the GDP, but this time INCLUDE the outlier
in your calculations. Show your work below.
Mean
Mean =
Median
Median =
SUPPORTING QUESTIONS:
Answer all supporting questions in complete sentences and justify your answers by
referring back to your calculations.
1) Look at your calculations for the mean and median when you DID NOT include the outlier.
 How many countries had a GDP less than the mean GDP?
 How many countries had a GDP greater than the mean GDP?
 How many countries had a GDP less than the median GDP?
 How many countries had a GDP greater than the median GDP?
2) Look at your calculations for the mean and median when you DID include the outlier.
 How many countries had a GDP less than the mean GDP?
 How many countries had a GDP greater than the mean GDP?
 How many countries had a GDP less than the median GDP?
 How many countries had a GDP greater than the median GDP?
3) Look at your answers for questions #1 and #2. When the GDP of the United States is
included in the calculations, which measure of central tendency (mean or median) most
accurately represents the GDP of a TYPICAL country in the top ten?
CLASSWORK 1.9
NAME:
PERIOD:
CONCLUDING QUESTIONS:
Now that you have examined three sets of data you are ready to make some general
conclusions. Answer each question in complete sentences and justify your answer by
referring back to calculations you made with the data sets.
1) When there is an outlier in a data set, how is the value of the mean affected? How is
the value of the median affected? Does the outlier have a greater affect on the mean
or the median? Remember to justify your answer with examples from your
calculations.
2) You want to accurately represent a typical number in a data set. If there is an outlier
in the data, which measure of central tendency (mean or median) should you use to
represent the data?
BONUS: In all our data sets the outlier was significantly higher than the rest of the data
points. An outlier can also be a data point that is significantly lower than the rest of the
data. How do you think that an outlier that is lower than the rest of the data will affect
the mean? How will it affect the median?