Mean Median Mode Range Predict Patriots' Super Bowl Score

Last week we looked at the 26 records either broken or tied during the Patriots win in Super Bowl LI. Could the Patriots win and score have been predicted by the last ten Super Bowl scores using measures of central tendency?

When you get a big set of data there are all sorts of ways to mathematically describe the data. The term "average" is used a lot with data sets. Mean, median, and mode are all types of averages. Together with range, they help describe the data. 

Definitions: 

Mean - When people say "average" they usually are talking about the mean. You can figure out the mean by adding up all the numbers in the data and then dividing by the number of numbers. For example, if you have 12 numbers, you add them up and divide by 12. This would give you the mean of the data. 

Median - The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number. If there is an even number of data points, then you need to pick the two middle numbers, add them together, and divide by two. That number will be your median. 

Mode - The mode is the number that appears the most. There are a few tricks to remember about mode: If there are two or more numbers that appear most often (and the same number of times) then the data has two or more modes. If there are two modes, this is called bimodal. If there are more than two modes, then the data would be called multimodal. If all the numbers appear the same number of times, then the data set has no modes. 

Range - Range is the difference between the lowest number and the highest number. The lowest number is called the minimum and the highest number is called the maximum. Take, for example, math test scores. Let's say your best score all year was a 100 and your worst was a 75. Then the rest of the scores don't matter for range. The range is 100-75=25. The range is 25. 

Example problem finding mean, median, mode and range: 

Find the mean, median, mode and range of the following data set:

9,4,17,4,7,8,14 

Finding the mean: First add the numbers up: 9+4+17+4+7+8+14 = 63. Then divide 63 by the total number of data points, 7, and you get 9. The mean is 9. 

Finding the median: First put the numbers in order: 4, 4, 7, 8, 9, 14, 17 The middle number is 8. Therefore, the median is 8. 

Finding the mode: Remember the mode is the number that appears the most. It can help to put the numbers in order so we don't miss anything: 4, 4, 7, 8, 9, 14, 17. The number four appears twice and the rest of the numbers only appear once. The mode is 4. 

Finding the range: The lowest number is 4. The highest number is 17. Range = 17 - 4. Range = 13. Remember, the lowest number is called the minimum and the highest number is called the maximum.

The first pdf attached has the definitions of each term with an example as well as the scores of the last ten Super Bowl games prior to the Patriots winning Super Bowl LI, 34-28. The pdf also has a word and definition matching practice. The second and longer pdf has many pages of practice for each of these concepts.  Grades 1-2 can just focus on page one and they do not have to try to find the mean or average since that requires division; of course, if they feel comfortable trying this, they should attempt the challenge.

Grades 3-6 should attempt as many of these challenges as possible including the word problems regarding the Super Bowl scores. These are very challenging but I provided answer keys for each challenge.

Now for the question that I posed at the beginning of this post: Could the Patriots win and score have been predicted by the last ten Super Bowl scores using measures of central tendency? The mean winning and losing scores of the past ten Super Bowls was 28.5 and 18.6, respectively. The median winning and losing scores of the past ten Super Bowls was 28.5 and 17, respectively. The mode winning and losing scores of the past ten Super Bowls was 31 and 17, respectively. The winning mode seems to best approximate the Patriots winning score of 34 and the losing mean seems to best approximate Atlanta's score of 28 (but it is 9.5 points off).

Now, here is the real challenge: whenever the children see a set of data that they find interesting and are curious about the central tendency of the data, they should practice finding the mean, mean, and mode of the data to see which one best represents the data. This can be done by opening up any newspaper to the sports pages, weather page, or business section.