Lesson 4

Explore

 

So far in this module you have looked at a variety of measures of central tendency, including mean, median, mode, and trimmed and weighted mean. When data is collected it is often summarized using one or more of these measures of central tendency. Although all of these measures represent an average, you have learned that each of them communicates slightly different information about a data set.

 

How do you know which measure of central tendency to use to best represent or describe the distribution of data?

 

The measure(s) of central tendency you would use requires careful consideration. Your choice is dependent on the data you have and what you want to communicate about it. Sometimes you may come across a set of data where all, or none, of the measures of central tendency are appropriate.

 

One of the first things you need to ask yourself when looking at a data set and deciding on which measure(s) of central tendency to use is whether there are any outliers. If so, then this may greatly influence the mean and may not be the best choice of measure. Also, if there are outliers, does it make sense to include them in the calculations? Remember that this will depend on what you are trying to communicate about the data.

 

Self-Check 1

 

Which measure(s) of central tendency would be the most appropriate for each of the following scenarios? Explain your selection.

1. You plan to buy a new bat for your softball team. What length of bat should you buy? Answer 
2. You would like to determine the typical income for people in your town. Answer 
3. You would like to know the typical height of students in a Grade 12 classroom. Answer 
4. A restaurant sells three sizes of ice-cream cones. How much does the store make per cone? Answer 
5. Using your previous knowledge, give an example of a scenario where the following measure of central tendency would be used. Explain the reason for each of your selections.
   1. arithmetic mean
   2. median
   3. mode
   
   Answer

6. Under what conditions would a trimmed or weighted mean be more appropriate than an arithmetic mean? Answer