Should I use interpolation when finding median, and quartiles?

Question

I am a S1 maths (Edexcel) AS student in the UK. My question: Say we have a stem-and-leaf diagram with 26 values. We want to find the lower quartile. To get the marks for our specification, we need to find the [(n+1)/2]th value. This is the 6.75th value.

So I use interpolation to find the said value:

6th value + (0.75*difference between 7th and 6th values)=value of the lower quartile.

But my S1 textbook says you should round 6.75 to 7 and just give the 7th value as the answer.

So: Should I use interpolation or approximation?????

Thanks!

Answer 1

Your textbook is correct. The lower quartile of your sample must be one of the 26 values in your sample. There is no 6.75th value, so you round to the nearest sample value.

In general, the quartiles of a sample are members of that sample, which is why you shouldn't interpolate in this case.