# QTS Numeracy Model Solutions – Test 2, Q23

In this series of blog posts, we look at some of the detailed methods that you could use to tackle the questions on the QTS Numeracy practice papers from the Department for Education.

In this post, we look at question 23 from practice test 2. The full practice paper can be downloaded here​.

## The Question

A teacher presented the following box-and-whisker diagram as part of a staff discussion on pupils’ performance. The diagram shows the percentage test marks in mathematics for a revision test for two class groups. Tick all the true statements:

• The range of percentage marks was greatest in class A.
• The median percentage mark in Class A was 15 percentage points less than the median percentage in Class B.
• The interquartile range was the same in both classes.

## Worked Solution

This is a question on box plots, which is a type of graph that you might come across that conveys some specific pieces of information to you.

In particular, the upper and lower ends of the ‘whiskers’ show the highest and lowest percentage scores achieved. The line in the middle of the box shows the median (the score that half of students achieved above and half below), and the two ends of the box show the upper and lower quartiles (the scores the one-quarter and three-quarters of students respectively scored above).

To answer this question, consider each of the statements in turn.

​The range of percentage marks was greatest in class A.

The range is the difference between the highest score and the lowest score, so you will need to read these values off the box plot for each graph and subtract them.

For class A, the highest score was 60% and the lowest score was 30%, so the range is 60% – 30% = 30%.

For class A, the highest score was 60% and the lowest score was 35%, so the range is 60% – 35% = 25%.

The range for class A is greater than the range for class B, so the statement is TRUE.

The median percentage mark in class A was 15 percentage points less than the median percentage in class B.

To find the median, read off the value of the line in the middle of the box.

For class A, this is at 45% and for class B, it is at 50%.

The difference between these values is 50% – 45% = 5%, so the statement is FALSE.

The interquartile range is the same in both classes.

The interquartile range means the difference between the value of the upper quartile and the lower quartile.

Read these values off the box plot by looking at the top and bottom of the box, and then subtract the values.

For Class A, the upper quartile is 50% and the lower quartile is 40%, so the interquartile range is 50% – 40% = 10%.

For Class B, the upper quartile is 55% and the lower quartile is 45%, so the interquartile range is 55% – 45% = 10%.

These values are the same, so the statement is true.

## Final Answer: True, False, True

Note – I have made a point of being thorough in this method to ensure you understand each point as we go. When you sit your QTS Skills Tests, your process will probably be much quicker as these techniques start to become second nature to you.

## Further Help

If you require any further help with questions like this, we have created a selection of resources to provide all the help you need.

Revision Book – The Guide to the QTS Skills Tests book devotes a whole chapter to each QTS numeracy topic, with detailed methods, worked examples and plenty of practice questions for you to have a go at. The book also includes three practice tests and fully worked solutions to every question.

Practice Tests – Want more practice tests to see how ready you are? Take a look at our selection of practice papers for the QTS numeracy test (including some totally free papers as our gift to you).

Revision Cheat Sheets – Our cheat sheets boil down everything you need to know to just the key points on the topic. They are a perfect resource for your last minute revision!