# RE: Help with Mode and Median

Discussion in 'Mathematics' started by siddons_sara, Apr 24, 2014.

1. ### siddons_sara

There seems to be some debate about what happens with modes:

mathforum.org/.../61375.html

whilst Wolfram Alpha ducks the issue here:

mathworld.wolfram.com/Mode.html

I've seen the set 1, 2, 3, 4, 5 described as having both 'no mode' and as being 'multimodal' with modes of 1, 2, 3, 4, 5.

On the GCSE papers, an example such as 2, 2, 3, 4, 4 is as difficult as it gets with modes of 2 and 4.

Most GCSE textbooks I've seen, if they cover the issue, go for no mode with the set 1, 2, 3, 4, 5. I'd always thought the same thing but after reading the Dr. Math post I was a little more doubtful.

What do others think?

2. ### PaulDGOccasional commenter

It's about the statistics working for you and not the other way round.

If the sample has 2 modes then, in most real situations, that's important - it's indicating there may be something "going on" in the population that has resulted in 2 points in the distribution that can be regarded as "central" and not one.

In a factory process it could be indicitive of a machine that has developed a fault so that it has 2 stable states at a setting (a limiting stop could have a worn thread, etc.).

In animal populations it's likely to indicate the sample contains more than one species or to point to male/female differences, etc.

So rather than the question being "what's the right answer?" the question is really "what have we uncovered about the population from this sample?" (Which is what all statistical questions are about!)

3. ### siddons_sara

Many thanks for the reply PaulDG, and I agree completely with what you have written. I really liked your practical example.

I'm still curious to know about the set 1, 2, 3, 4, 5 being described as having both 'no mode' and as being 'multimodal' with modes of 1, 2, 3, 4, 5. Or the set 1, 1, 2, 2, 3, 3, 4, 4, 5, 5?

4. ### PaulDGOccasional commenter

It's the same thing - a result like this means you need to look behind the data in the sample to understand if this is telling you anything useful.

In both your sample sets, the values 1,2,3,4,5 have the same frequency. What does that mean when consider the potential mechanisms operating in the population?

Are 1,2,3,4,5 the only possible values? In which case, the interpretation that there's "no mode" seems likely to be the most useful one - your sample appears to be indicating that all possible values are equally probable.

Or are there other possibilities? Then the fact that the samples contain these particular 5 values and that they occur with equal probability would suggest that there are 5 equally modal modes.