# Rounding to find data point for quartiles

Discussion in 'Mathematics' started by upamountain, Sep 12, 2015.

1. I'm a non-specialist teaching S1.

My students know how to find Q1, median and Q3 but love bombarding me with the same question over and over again about why we round UP if we have a non-integer value of n/4 etc. (e.g. if n is 9, we round 2.25 up to find the 3rd data point for Q1).

I know some of the students just love asking the question because they think they sound cleverer than me "so I always round 2.2 up to 3 then Miss" (in a sarcastic tone) etc. However, I know that some are genuinely confused. (There are some weak students in the group).

Any ideas? Thanks!

2. Draw nine boxes, for the nine pieces of data.

Draw an arrow pointing to the halfway point, and two more at the quarterway points. Which boxes are these pointing at?

3. I'd disagree that Q1 is the third data point. If you have 9 data points then the 5th is the median, leaving four data points below it. The middle of these four data points would be between the 2nd and 3rd data points, and so Q1 is the 2.5th data point.

4. It's usually the case that there are either 4n or 4n-1 data points.

So if there are say 12, Q1 at 3.5, Q2 at 6.5, Q3 at 9.5 - equal numbers of data points between the quartiles

And if there are say 11, Q1 at 3, Q2 at 6, Q3 at 9 - again equal numbers

If there are 13 or 14 then *different statisticians disagree about how to find the quartiles*. This is really important. There is not one RIGHT way of doing it. You can teach students a method, but it's not gonna happen in S1, there will be 4n or 4n-1. Guaranteed.

5. I remember being told at an AQA GCSE course that they always gave 4n-1 points, so that it would be like adamcreen's second example. I have no idea if this is still true or true for other boards. MEI S1 mark schemes seem to allow more than one answer.

As a non-statistician, I would query the value of finding quartiles for small data sets, and for large data sets, who cares?! It makes so little difference.