Mean Versus Median

Before 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 theaverage 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?

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:

89879390129188878391

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 first- year contract offers to play in the National Basketball Association (zero indicates that the player did not receive a contract offer):

0000$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

Explanation

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'sclaim 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?

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 thinkof all the possibilities that can occur and if you need to, "create" a data set to help you determine which "average" to choose.

Scenario

Explanation

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