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:

Calculate mean, median, and mode of various data.

Explore the measures of center (mean, median, and mode) and determine which “average” (mean or median) would be a better representation of data given.

Understand that data can be skewed.

Apply your knowledge to real-life problems and explain how a single number can represent the nature of data.

Procedure:

As you work through the Part I Activity, here are some guided questions to help you in your endeavor.

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:

How did Sarah calculate her answer?

How did Andrew calculate his answer?

Who do you believe is correct and why?

In this particular scenario, what does the term “average” mean?

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?

For problem #2, determine how Mrs. Smith’s class performed on a particular quiz.

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?

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?

For problem #3, explain why the statement made by the college is misleading. Here are some guiding questions to help you along the way:

Part A:

Just by looking at the data, what do we know about the 5 basketball players? Did they all receive a contract?

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?

Results: Complete the Student Worksheet and turn in your completed worksheet on Canvas.

Results: Complete the Student Worksheet and turn in your completed worksheet on Canvas.

Part B:

How else could we calculate the “average”? Why would this “average” be a better representation of the data?

How does the $10,000,000 affect the dataset as a whole? What kinds of numbers drastically affect the dataset?