Mean, Median, Mode: Which One?

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  • 1. The 3 Ms of Central Tendency Mean, Median, and Mode Which one should you use?Image retrieved 3/25/2012. From http://m-m.seebyseeing.net/
  • 2. 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
  • 3. 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
  • 4. 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?
  • 5. 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.
  • 6. Which M, M, & M would be bestfor… The favorite movie of college students?
  • 7. Which M, M, & M would be bestfor… The favorite movie of college students? Mode: good for non-numerical data items and for frequent occurrences.
  • 8. Which M, M, & M would be bestfor… The distances students in your class travel to school. Retrieved from http://openclipart.org/detail/21980/toy- car-by-nicubunu 4/7/2012
  • 9. Which M, M, & M would be bestfor… 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
  • 10. 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
  • 11. 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
  • 12. 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.
  • 13. 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!
  • 14. http://www.khanacademy.org/math/statistics/e/exploring_mean_and_median Below is a sample problem from the Khan Academy website above.