The 3 Ms of Central Tendency

Mean, Median, and Mode

Image retrieved 3/25/2012. From http://m-m.seebyseeing.net/

Which one should you use?

Why Does It Matter?

You live in a town of 1,000 people where the mean income is $25,000 and the median income is about the same.

Retrieved from http://en.wikipedia.org/wiki/Damascus,_Virginia 4/7/2012

Why Does It Matter?

Now the mean income is $1,023,976, but the median income is still about $25,000.

Retrieved from http://genehoyas.com/ 4/7/2012

The Town of Millionaires

It is a wonderful story about this whole town of millionaires who are so frugal they live in ordinary homes. What a great example of America!

Why is this misleading?

Why Does It Matter?

Most people in this town are still pretty poor.

The mean does not give a good picture of the “typical” resident.

This could be a big deal if the town loses government services because of its income level…but we will hope whoever is in charge of those numbers does a little better research.

Which M, M, & M would be best for…

The favorite movie of college students?

Which M, M, & M would be best for…

The favorite movie of college students? Mode: good for non-numerical data items

and for frequent occurrences.

Which M, M, & M would be best for…

The distances students in your class travel to school.

Retrieved from http://openclipart.org/detail/21980/toy-car-by-nicubunu 4/7/2012

Which M, M, & M would be best for…

The distances students in your class travel to school.

Median: one student may live much further than everyone else. When an outlier may significantly influence the mean, we use median.

Retrieved from http://openclipart.org/detail/21980/toy-car-by-nicubunu 4/7/2012

Which M, M, & M is best?

The daily high temperature during a week in July.

Retrieved from http://activerain.com/blogsview/1205564/too-hot-to-blog-dog-days-of-summer 4/7/2012

Which M, M, & M is best?

The daily high temperature during a week in July.

Mean: since daily temperatures are not likely to have an outlier, mean is best. When data have no outlier, use mean.

Retrieved from http://activerain.com/blogsview/1205564/too-hot-to-blog-dog-days-of-summer 4/7/2012

Summary

When data have no outliers, we typically use mean.

When data have outliers, we choose median.

When we are interested in the frequency of particular values or we want to summarize non-numeric data, we use mode.

Measures of Central Tendency

Go to the Khan Academy site whose web address appears on the next slide and work with the data to achieve the requested values for the mean and median.

This will help you determine the effect changes in data have on those measures.

Knowing this will help you figure out which M works with the data best!

http://www.khanacademy.org/math/statistics/e/exploring_mean_and_median

Below is a sample problem from the Khan Academy website above.