Calculate Percentiles and Quartiles

If your test score is in the 90th percentile, what does that mean?

It means that 90% of the students scored below you!

You must have studied really hard then!!

Percentiles always tell us the percentage of the data that is under or equal to a certain value.

Let's have a look at an example:

The scores (out of 100) of 12 students in a class are:

65, 70, 72, 75, 78, 80, 82, 85, 88, 90, 92, 95

Find the 75th percentile.

75th percentile means the score such that 75% of the scores are under or equal to it.

Here, there are 12 students in total and since 75% = 3/4, we have:

75% of 12 = 3/4 of 12 = 9

So we want the score such that 9 scores are under or equal to it, so we essentially want the 9th score when ordered from smallest to the largest.

The 9th score is 88 and the 8th and 10th are 85 and 90.

So 88 is a score such that 9 scores (i.e. 75% of the scores) are under or equal to it.

Our 75th percentile here is then 88!

It's confusing, but will come clearer as we try out the questions!

The 75th percentile is one of three special percentiles that we call quartiles.

These are simply the percentiles that divide the data into four quarters (hence the word 'quartile'):

Lower quartile = 1st quartile (Q1) = 25th percentile, i.e. value that 25% of the data are smaller or equal to

Median = 2nd quartile (Q2) = 50th percentile, i.e. value that 50% of the data are smaller or equal to

Upper quartile = 3rd quartile (Q3) = 75th percentile, i.e. value that 75% of the data are smaller or equal to

Let's have a go at some questions!