Transum Software

Quartiles

Practise processing the sets of numbers to find the lower and upper quartiles.
  Menu   Level 1 Level 2 Level 3 Level 4 Level 5 Level 6   Exam     Help     More  

This is level 6: Mixed problem-solving questions.

You will be awarded a trophy if you get at least 7 answers correct and you do this activity online.

1

Find the interquartile range of the following data set:

$$1, 5, 5, 5, 2, 1, 6, 2 $$

☐ ☐ ✓ ✗

2

Find the interquartile range giving your answer rounded to 2 decimal places:

$$ \frac{7}{8} , \frac{3}{4} , \frac{15}{16}$$

☐ ☐ ✓ ✗

3

Find the upper quartile of all the two digit square numbers.

☐ ☐ ✓ ✗

4

Find the interquartile range of all the prime numbers between 10 and 40

☐ ☐ ✓ ✗

5

Find the value of \(x\) if the lower quartile of this data set is 21:

$$31, 22, 47, x, 58$$

☐ ☐ ✓ ✗

6

Find the value of \(y\) if the uper quartile of this data set is 15.5:

$$4.6, y, 12, 3.2, 8.9, 21.1, 10, 17.3 $$

☐ ☐ ✓ ✗

7


$$22z, 3z, 15z , 30z, 7z$$

Given that \(z\) is a positive number and the interquartile range is 42 find the value of z

☐ ☐ ✓ ✗

8

$$w-3, w+11, w-12,\\ w+7, w+11, w+2, w-1, w+7$$

Given that \(w\) is a positive number and the upper quartile is twice the lower quartile find the value of \(w\)

☐ ☐ ✓ ✗

9

ContinentArea (million km²)
Africa30.37
Antarctica14.00
Asia44.58
Europe10.18
North America24.71
Australia8.56
South America17.84

Find the value of the upper quartile area of the continents in millions of square kilometres.

☐ \( \text{million km}^2\) ☐ ✓ ✗

10

PlanetMass (kg)
Mercury3.3011 × 1023
Venus4.8675 × 1024
Earth5.9724 × 1024
Mars6.4171 × 1023
Jupiter1.8982 × 1027
Saturn5.6834 × 1026
Uranus8.6810 × 1025
Neptune1.0241 × 1026

Find the interquartile range to three significant figures.

☐ \( \times 10^{26} \text{ kg}\) ☐ ✓ ✗

Check

City Scape

This is Quartiles level 6. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 5

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 24 May 'Starter of the Day' page by Ruth Seward, Hagley Park Sports College:

"Find the starters wonderful; students enjoy them and often want to use the idea generated by the starter in other parts of the lesson. Keep up the good work"

Comment recorded on the 14 October 'Starter of the Day' page by Inger Kisby, Herts and Essex High School:

"Just a quick note to say that we use a lot of your starters. It is lovely to have so many different ideas to start a lesson with. Thank you very much and keep up the good work."

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.
Featured Activity

Connect 4 Factors

Connect 4 Factors

A mathematical version of the popular Connect 4 game based on getting four numbers with a common factor in a line. Fun for one, two or a whole class of pupils.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there is a mirror site at Transum.info that contains most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

For Students:

 

For Teachers:

For All:

Transum.org is a proud supporter of the kidSAFE Seal Program
©1997-2024 WWW.TRANSUM.ORG

© Transum Mathematics 1997-2024
Scan the QR code below to visit the online version of this activity.

This is a QR Code

https://www.Transum.org/go/?Num=174

Description of Levels

Close

❎

Medians - Find the medians (\( Q_2 \)) of sets of different types of numbers.

Level 1 - Number sets containing 5 positive integers

Level 2 - Number sets containing 6 positive integers

Level 3 - Number sets containing 7 positive integers

Level 4 - Number sets containing 10 positive and negative integers

Level 5 - Number sets containing positive and negative decimals and fractions

Level 6 - Mixed problem-solving questions

Box Plots - An exercise on reading and drawing box-and-whisker diagrams which require a knowledge of quartiles.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Method for Finding the Quartiles

For discrete distributions, there is no universal agreement on selecting the quartile values, but for the purpose of this exercise, we'll use the most popular method:

  1. The median is the value in the middle of the data set when it is arranged in order of size.
  2. Use the median to divide the ordered data set into two halves. The median becomes the second quartile.
  3. If there are an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half.
  4. If there are an even number of data points in the original ordered data set, split this data set exactly in half.
  5. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

The interquartile range is the difference between the upper and lower quartiles: \( IQR = Q_3 - Q_1 \).

Outliers are the points lying beyond the upper boundary of \(Q_3 + 1.5 \times IQR\) and the lower boundary of \(Q_1 - 1.5 \times IQR\).

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

Close

❎