Mean, median, and mode

Tutoring high school math, you deal with introductory statistics.  The tutor introduces measures of central tendency.

Let’s imagine you have the following seed counts from eleven different apples:

15 9 8 10 8 10 8 5 7 14 12

We wish to find the mean, median, and mode of the seed counts.

When I was a kid, people said “average” instead of mean. To find the mean, we add all the numbers together, then divide by how many there are (in this case, 11):

mean=(15+9+8+10+…..+14+12)/11=9.6363…

So, the mean number of seeds in the apples is 9.6363…

To find the median, you line up the numbers from least to greatest. The median is the middle one.

We rewrite the numbers in ascending order:

5 7 8 8 8 9 10 10 12 14 15

The middle number is 9. Therefore, the median number of seeds in the apples is 9.

The mode is simply the count that occurs most often. In this case, it’s 8. At three times, 8 happens more than any other count.

Some points to note:

  1. At 9.6363….., the mean doesn’t actually occur in the data set. Very often, such is the case.
  2. What if the list has an even number of entries? An odd-numbered list has a clear “middle” one, but an even-numbered list doesn’t.
  3.  
    Consider the following list of six entries:

    5 6 7 10 13 14

    Here, the median is (7+10)/2=8.5. To find the median of an even list, you take the two middle values, add them, then divide by two.

  4. What if, as in the six-membered list just above, there is no “most frequent” value? What is the mode in such a case?
  5.  
    For the six-membered list just above, you can see it in two ways: either there’s no mode, or else there are six different modes. However, consider the following list:

    1 1 2 3 5 6 7 7 9

    For this list, we would say there are two modes: 1 and 7.

The mean, median, and mode are all called measures of central tendency: they all estimate what the “next” value would be. I’ll be saying more about them in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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