Mean Versus Median Worksheet

Mean Versus MedianBefore you begin:
• Review how to calculate mean, median, and mode.
Background: As described by your readings, the term “average” is often used in multiple
contexts and does not necessarily mean taking the sum of your data and dividing by the number
of items in the dataset. Sometimes, the term “average” can be used to refer to other measures of
center, such as the median or the mode. In this activity, we will explore how the various
meanings of “average” and determine which measure of center would better represent the data.
In this activity you will:
1. Calculate mean, median, and mode of various data.
2. Explore the measures of center (mean, median, and mode) and determine which
“average” (mean or median) would be a better representation of data given.
3. Understand that data can be skewed.
4. Apply your knowledge to real-life problems and explain how a single number can
represent the nature of data.
Procedure:
1. As you work through the Part I Activity, here are some guided questions to help you in
your endeavor.
a. For problem #1, determine who is correct (Sarah or Andrew) in giving the
average price for a particular energy bar. These are some questions you should be
asking yourself:
i. How did Sarah calculate her answer?
ii. How did Andrew calculate his answer?
iii. Who do you believe is correct and why?
iv. In this particular scenario, what does the term “average” mean?
v. The price difference between Sarah’s calculations and Andrew’s
calculations may not be much, but can you think of an instance where it
would matter which “average” is used?
b. For problem #2, determine how Mrs. Smith’s class performed on a particular
quiz.
i. Part A: Before making any calculations, look at the data overall and give
your best educated guess as to how you think the students did on the quiz.
Which “average” do you think would best describe her students’
performance?
ii. Part B: Based on your observations in Part A, calculate the necessary
“average” you think will provide Mrs. Smith with the best feedback.
Which “average” did you choose and why? Now that you see the number
that represents the data, do you agree with your initial assessment in
Part A?
c. For problem #3, explain why the statement made by the college is misleading.
Here are some guiding questions to help you along the way:
i. Part A:
1. Just by looking at the data, what do we know about the 5
basketball players? Did they all receive a contract?
2. The college claimed that “the average senior on this basketball
team received a $2 million contract offer.” Which “average” are
they referring to? Do you agree/disagree with their statement?
Why or why not?
Part B:
1. How else could we calculate the “average”? Why would this
“average” be a better representation of the data?
2. How does the $10,000,000 affect the dataset as a whole? What
kinds of numbers drastically affect the dataset?
Results: Complete the Student Worksheet and turn in your completed worksheet on
Canvas.
Name:
Mean Versus Median
1) Sarah and Andrew were comparing prices of their favorite energy bar. Eight grocery stores
sell the PR energy bar for the following prices:
$1.09 $1.29 $1.29 $1.35 $1.39 $1.49 $1.59 $1.79
Sarah claims the average price of the candy bar is $1.37 but Andrew disagreed and said the
average price of the energy bar is actually $1.41. How did Sarah and Andrew come up with these
prices? Based on their calculations, who do you think is correct and why?
2) Ms. Smith, a math teacher, recently gave a mathematics quiz in her class. The ten quiz scores
were:
89
87
93
90
12
91
88
87
83
91
a) Based on the test scores above, would you say the class did well? Why or why not?
b) If you were Ms. Smith, which average would you use to describe the data: mean, median, or
mode?
3) Suppose that five graduating seniors on a college basketball team receive the following firstyear contract offers to play in the National Basketball Association (zero indicates that the
player did not receive a contract offer):
0
0
0
0
$10,000,000
The college claimed that the average senior on this basketball team received a $2 million
contract offer.
a) Explain how the college came up with this number and why this statement may be misleading.
b) Would another measure of central tendency be a better representative of the data? Support
your answer.
Analysis
1) As with the Part I Activity, determine which “average” would be a better fit for the data
given. Notice that the first two scenarios are very similar to those done in the activity.
Given a dataset, calculate and determine whether the mean or median would be a better
representation of the data. As you work through these two problems, be sure to calculate
BOTH the mean and median. Be careful in how you choose which “average” to use since
the question asks for a particular value.
Scenario
Mean Median
a) A retail store had total sales of $436,
$650, $530, $500, $650, $489, and $423
last week. Which measure of data would
make the store’s sales last week appear
the most profitable?
b) Suppose you have opened some
Nutty Bars to check the company’s
claim of an “average” of 8 peanuts per
bar. Here is what you found after
opening 10 bars: 5, 8, 8, 8, 11, 7, 8, 6, 6,
and 6. Which
average should the company use to
support their claim?
Explanation
2) For the second part of this activity, determine which “average” would be a better representation WITHOUT
being given a specific data set. This will require you to think about WHO is requesting or wants the data and
then determine which “average” would better suit their needs. In real-life settings, most companies like to
portray themselves in a better “light,” so you will have to think critically about how best to do that. Try to
think of all the possibilities that can occur and if you need to, “create” a data set to help you determine which
“average” to choose.
Scenario
a) The average number of pieces of lost
luggage per flight from an airline
company’s perspective
b) The average weight of potatoes in a
10- pound bag
c) The average age at first marriage for
men in America
Mean Median
Explanation