Math Background

Lesson: Mean, Median, and Mode
Introducing the Concept

Your students may have encountered mean, median, and mode before, but it's a good idea to review with students how to find these again. The mean, median, or mode is used by statisticians to find one number that is representative of all the numbers in a data set. Discuss with students the importance of finding one number that would be representative of all the numbers in a set.

Prerequisite Skills and Concepts: Students should be able to put a set of numbers in ascending or descending order and perform simple calculations using the four basic operations.

Write the following numbers on the board: 6, 3, 2, 5, 6, 14, 1, 2, 4, 5, 16, and 2.

  • Say: These numbers are the number of runs scored in the 12 games played by a middle school baseball team. I'd like us to analyze them for more information. What might I do with the data to help analyze the information?
    Students might suggest a number of things, such as making a graph, putting the numbers in order, finding the mean, median, or mode for the number of runs per game, and so on. If they don't, suggest some of those ideas to them.
  • Say: Someone suggested putting the numbers in numerical order. Let's do that.
    Have a volunteer come to the board and arrange the data in order from least to greatest: 1, 2, 2, 2, 3, 4, 5, 5, 6, 6, 14, 16.
  • Ask: Now that we have ordered the data, which one of the measures of central tendency would be easy to find from this list? (the median) How would I go about finding the median?
    Students should answer that since there are 12 numbers, the median is the average of the sixth and seventh numbers, which is 4.5.
  • Ask: What else is easy to find from the data on the board? (the mode) What is the mode of a set of data? (It is the number that occurs most frequently.) So what is the mode of this set? (2)
  • Ask: How would I find the mean of this data? (Add all the numbers and divide by 12.) At your desks, find the mean of the data.
    Indicate that the sum of the scores is 66 and that the mean is 5.5.
  • Ask: Are there any numbers that are much less or much greater than most of the other numbers? (yes, 14 and 16) Numbers like this are called outliers, because they are distant from most of the other numbers. What might cause this to happen in this case?
    Students may say that the opposing team didn't have a good pitcher or the defense was weak or something similar.
  • Say: Let's disregard the games with 14 and 16 runs and investigate the mean, median, and mode again. Would the mode change? (No, it would still be 2.)
  • Ask: What would the median be? (3.5) Find the mean of the new data.
    Give students time to compute the mean. (The sum of the 10 numbers is 36 and the mean is 3.6.) Be sure students divide by 10 and not 12, since there are only 10 numbers in the new data set.
  • Ask: What happened when we removed some outliers that were greater than most of the other data? (The median and mean got smaller, and the mode didn't change.)
  • Say: Depending on the data, we can't always be sure the mode will stay the same or that the median will become less, but we can be sure that the mean will get smaller if we eliminate outliers that are greater than most of the data. What do you think would happen to the mean of a set of data if we eliminated data that were much less than the mean?
    Students should say that the mean would increase.
Houghton Mifflin Math Grade 6