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Quartiles

Practise processing the sets of numbers to find the lower and upper quartiles.
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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.

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

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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.
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Description of Levels

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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.

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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.

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