Measures of Central Tendency

Measures of central tendency sometimes produce similar results and sometimes produce very different results.  Think about the solutions below and, without doing the math, explain how mode, median, and mean for each of the datasets will differ:

  1. Your family is shopping for houses  You know that you want to live in Torrance and you look at 15 houses that range in price from \$350,000 to \$470,000. However, one day you see an open house in Bel Air and you have to go visit that house with the 2 pools and the private movie screening room.  That house lists for \$4.5 million dollars. How will the mode, median, and mean of the list prices of the houses you looked at differ? What measure captures the "normal" house price the best? The worst?
     
  2. Over the course of the semester you have taken 10 tests.  You've gotten two perfect scores of 100.  The rest of your scores have ranged from 85 to 99, spread out pretty evenly, but surprisingly, other than the 100s, you have never gotten the same score twice.  How will the mode, median, and mean of your scores differ?  What measure captures your "normal" score the best? The worst?
     
  3. All of your friends are pitching in to pay for a party. Of your group of 30 friends, almost all have contributed 20 dollars.  Two of your friends have good jobs and they put in 50. One friend is always a slacker and hasn't put in anything. How will the mode, median, and mean of the amount of money your friends pitched in differ? What measure captures the "normal" amount the best? The worst?
     
  4. You are shopping for coats.  You are looking at two coats at Ross for \$39.99.  There is a great coat at Forever 21 for \$27.99.  Macy's has another coat for \$56.99. The GOOP website has a truly amazing coat for \$8,690. How will the mode, median, and mean of coat prices differ? What measure captures the "normal" price the best? The worst? 
     

In the following scenarios, what could be causing the differences in measures of central tendency?

  1. A teacher is looking at the SAT scores for her class.  She's puzzled by the results. The mode score is 2000, which is amazing. The median score is 1800, which is still pretty good. But, the mean score is 700. What could have happened to create these three different measures?
     
  2. A student is working hard in AP Calculus. He learns that his median test score is 80 and he's thrilled that he will get a B. But, then his grade is a D. Baffled, he goes to his teacher and his teacher says that he's sorry, but he bases grades on an average (or mean) and not a median. What could have caused these scores to be so different?
     
  3. In Mississippi, the mean household income is approximately \$20,000/year.  The median household income is approximately \$38,000/year. What could explain the differences between these two numbers?
     
  4. In Orange County, California, the median household income is approximately \$34,000/year.  The mean household income is approximately \$75,000/year? What could explain the differences between those two numbers?
     
  5. Thinking about income would mode be a good way to judge the "typical" household income in a state or county? Why or why not?
     

Answer Key: