Math CentralQuandaries & Queries


Question from Kaliela, a student:

Can the Median > mode > mean?
Can the Mean > Mode > Median?
I don't think either of these can occur but I'm unsure why?

Hi Kaliela,

I would look for examples.

Let's say that in my data set every number appears once except 10 which appears twice. Thus the mode is 10. In the first example you want the median less than the mode so there must be at least two observations less than 10. Maybe your data set looks like

data set 1

But in this case all 4 observations are less than or equal to 10 so the mean will be less than or equal to 10. You need some observations larger than 10 but every time you add an observation larger than 10 you need to add one less than 10 to keep the median less than 10, maybe like

data set 2

Now try some particular numbers, maybe X = 7, Y = 8, Z = 9, W = 11. What is the mean? How can you change one number to force the mean to be larger than 10?



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