How do you find the upper and lower quartiles?

Question

Yes, I realise I now look stupid for asking such a simple question, but hey, we all forget things and you get an easy 2 points for it =]. So how do you find the lower and upper quartiles of a set of data without drawing a cumulative frequency chart?

Answer 1

First put numbers in order. Then find median - if you have 10 numbers do (1+10)/2 = 5.5 , average of 5 and 6 . For 13 numbers do (1+13)/2 =7. And so on, same rules apply for all even / odd sets of numbers. Just imagine them as the numbers 1,2,3,4,.... in sequence.
Your numbers are now split into an upper and lower band and you can follow the same logic to find both upper and lower quartiles .

With 10 numbers lower band is 1-5 add and then halve - 3. Upper band is 6 -10 and upper quartile is 8.
Check that gaps between quartilles are same.

For number set of 13 upper / lower band numbers are 1 - 6 and 6- 13 so quartiles are 3.5 and 9.5 respectively again take half way between the actual numbers.

Illustration below indicates final distribution:

1 2 / 3 4 / 5 6 / 7 8

Gaps are equal and lower / upper quartiles are 2.5 and 6.5

Answer 2

The way I would do it is to put all the data in order, in one long list (eg. one column in Excel)

Then count up one quarter of the way (and down one quarter).

Answer 3

organise the data in order and take the quarter and three quarter value