Real Life Examples – What’s the Average?Aliya recently moved to Dearborn, MI. Her family is looking to buy a home in the neighborhood where her grandmother lives. The area has many middle-eastern stores and the famous Shatila bakery, that has the best baklavas and pastries, is close by. Aliya finds out that the owner of Shatila also lives in the neighborhood. Below are homes on a block in the area where Aliya’s family is looking to buy their new home. What is the average price of the home on this block?

$40,000

$50,000$47,000

$43,000

$45,000 $42,000

$640,000

MEAN Home Price: $(40,000 + 45,000 + 42,000 + 50,000 + 47,000 + 43,000 + 640,000)7

MEAN = $129, 571.43

MEDIAN Home Price: $40,000, $42,000, $43,000, $45,000, $47,000, $50,000, $640,000MEDIAN = $45,000

THERE IS NO MODE FOR THIS DATA.

WHICH ONE REPRESENTS AVERAGE HOME PRICES BETTER AND WHY?

Pretend you are the realtor and are showing homes in the neighborhood. What would you quote as the average price of a home in the neighborhood and why?Some questions for the realtor to consider:1. What is the price range within which Aliya’s family can afford to buy a home?2. Based on the affordability factor, would the mean, median or mode be most appropriate

average to quote?3. How does the price of the home of the owner of “Shatila” bakery affect the calculation of

average (OUTLIER)?4. Which measure is affected by the unusually high price of one home?

Recall:MEAN = $129, 571.43MEDIAN = $45,000MODE = NONE

CASE 1: Let’s pretend that Aliya’s family can afford a home up to $130,000. Would you as the realtor interested in making a sale fast quote 1) the mean price or 2) the median price and why?

CASE 2: Let’s pretend that Aliya’s family can afford a home up to $50,000.

Would you as the realtor interested in making a sale fast quote 1) the mean price or 2) the median price and what would your justification be?

Write answers to the following questions in your Math Journals

Dejaun met seven graduates from University of Michigan, Ann Arbor, who majored in communications and recently found jobs. Dejaun is considering a career in communications and therefore he asked them about their beginning salaries. Dejaun found out that the salaries were:(Dr. Ian (2003), http://mathforum.org/dr.math/ )

$27,000, $29,000, $33,000, $34,000, $35,000, $39,000, $5,000,000 The last guy got a job playing basketball in the NBA ($5,000,000 = OUTLIER)!

MEAN = $7,42428.57 MEDIAN = $34,000

• Would the mean or median be a better representation of what Dejaun could expect to earn after graduating as a communications major?

• On the other hand if some recruiter had quoted the mean as the average salary of a communications major, would he have been able to recruit more people? Would it serve students to find out what measure is being quoted and what data it was based on before making such decisions?

Real Life Examples – What’s the Average?

Write answers to the following questions in your Math Journals

The seventh graders at Hill Valley Middle School are planning a camping trip to Howell Nature Center in the Fall. Students plan to earn the money over summer and are trying to determine how many hours they need to work in order to earn the $200 they need for the trip. They survey 10 seniors and collect the following data regarding the numbers of hours the seniors worked in order to earn money for this trip the past summer. What is the average number of hours a student needs to work over the summer to earn $200?

Calculate the mean, median and mode.

MEAN = 15.4 hoursMEDIAN = 13 hoursMODE = 0 hours

Student Number of Hours Worked During Summer

1 0

2 4

3 25

4 11

5 6

6 32

7 21

8 0

9 40

10 15

On average, how many hours would a student have to work if they had to earn $200?

Some questions for students to consider:

1) How well do the mean, median or mode represent the data collected by the students?

2) Did students collect other information along with the number of hours worked, such as the kind of jobs students worked at and the pay they received?

3) Would it be wise to check their savings and any possible contributions from their family?

4) Would it be more appropriate to decide the number of hours they would have to work based on what kind of jobs they were interested in, allowed to do by their parents and were available to them?

Student Number of Hours Worked During Summer

1 0

2 4

3 25

4 11

5 6

6 32

7 21

8 0

9 40

10 15

MEAN = 15.4 hoursMEDIAN = 13 hoursMODE = 0 hours

Write a paragraph stating what information you would consider to figure out how much money you would need to earn and how. Justify your reasoning using the data from this example.

Think About ItMedian vs. Mean: Know the Difference or Risk Being Manipulated(Darwin, 2009)The definition of median and mean and the difference between the two terms is poorly understood by many people and while in many data sets, there is only a marginal difference between the two from a practical standpoint, there is sometimes a stark difference between the two. People toss around terms like “average”, mean, median and other statistical terminology without either understanding what they’re talking about themselves, or with the intent to silence critics with ‘fact’. Understand that various entities routinely manipulate how a piece of data is presented in order to beguile you, the recipient, in order to advance their agenda.

Median Mean – What’s the Difference?This is why it's important to understand that when someone reports an "average" value, he/she might be talking about the mean, the median, or the mode, depending on what kind of impression he wants to make. It's up to you to ask, in each case,which average he's talking about.