# Understand Percentiles and Quartiles

In this worksheet, students will calculate percentiles and quartiles.

Key stage:  KS 3

Curriculum topic:   Statistics

Curriculum subtopic:   Understand Variables, Representation, Measures and Spread

Difficulty level:

#### Worksheet Overview

How tall are you?

The heights (in centimetres) of 10 students were collected:

151, 153, 154, 155, 157, 163, 168, 168, 169, 170

What percentage of students are shorter than 156 cm?

We can see that there are 4 heights that are under 156 cm.

This is out of 10 students in total, so the proportion of those students is 4/10.

We can convert this to a percentage by either making the denominator 100 and reading off the numerator or multiplying the fraction by 100:

4/10 = 40/100 so 40% students are shorter than 156 cm

or

(4/10) x 100 = 40 so 40% students are shorter than 156 cm

We call this 156 cm the 40th percentile.

It means that 40% of the students' heights are under or equal to 156 cm.

We could also say that 60% of the students' heights are above it.

Similarly, we could get any percentile, not just the 40th!

For example, the 80th percentile means 80% of the data is under or equal to the value that is the 80th percentile.

Above, we found what percentile 156 cm is.

But we can also go the other way around and find what number would be a given percentile!

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!

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'):

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

2nd quartile (Q2) = 50th percentile, i.e. value that 50% of the data are smaller or equal to - so it is the middle value, i.e. the median

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

That's quite a lot of information, isn't it?!

But don't worry, you can always come back to this introduction by clicking on the red help button on the screen.

Let's have a go at some questions, shall we?

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