Lesson 1 - Quartiles and the interquartile range

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Introduction

In this lesson you will:

revise mean, median and mode
be introduced to quartiles and the interquartile range
apply your understanding of these by playing a game.

Overview

Duration: 2:51

Watch this video in full screen.

Activity 1 - Revision of mean, median and mode

Before we start learning about quartiles and interquartile range, we need to revise our understanding of the measures of central tendency:

mean
median
mode.

Task 1

Watch this Eddie Woo video to review the differences between mean, median and mode.

Measures of Central Tendency (1 of 2: Comparing Mean & Median)

Duration: 15:25

Need more information to help you understand?

Then read the following pages on the Maths is Fun website to refresh your knowledge further:

Task 2 - Exploring mean and median

Use the following Desmos interactives to explore mean and median. Answer the questions in Parts 3, 6 and 7 in your exercise book or folder.

Note: To use the the interactives you need to open each link in a new tab by clicking on the image. If the folder tab is open on the left hand side of the screen close it so you can see the number line in full screen.

Part 1: Finding the mean 1

Move the points left and right so that they have a mean value of 8.

Image link to desmos activity Finding the mean

Part 2: Finding the mean 2

Choose points that have a mean of 8 but a range as big as possible.

Image link to desmos activity Finding the mean (2)

Part 3

If 4 data points have a mean value of 3, what must be true about any, or all of the points?

Part 4: Finding the median 1

Drag the points so that the median value is 8.

Image link to desmos activity Finding the median

Part 5: Finding the median 2

Drag the points so that the median value is 6 and the range is as large as possible.

Image link to desmos activity Finding the median (2)

Part 6

What values most affect the median?

Part 7: Impact of outliers

Drag a point until it is much higher or lower than the others. What effect does this have on the mean and median?

Extension activity

Create a set of five positive integers from 1 to 20 that have the same mean, median, and range.

Remember: range is the highest number minus the lowest number.
Need a hint or the answer? Visit this activity, Mean, Median and Range on the Open Middle website.

Activity 2 - Introduction to quartiles and interquartile range

Task 1

Watch these two Eddie Woo videos on the introduction to quartiles and the interquartile range.

Measures of Spread (1 of 2: Range & IQR)

Duration: 8:02

Measures of Spread (2 of 2: How to find Inter-Quartile Range)

Duration: 11:32

Task 2

Complete the following task in your exercise book or folder. Remember to show your working.
Find the quartiles and interquartile range for these sets of data. Remember to place the data in order from smallest to biggest before you start.

Set A: 2, 5, 6, 8, 10, 11, 15, 15,16, 17, 20, 25
Set B: 3, 6, 8, 9, 9, 11, 15, 16, 17, 18, 20, 23, 25
Set C: 4, 6, 1, 5, 11, 21, 25, 17, 20, 15, 19, 2

Task 3

Click on the image to open the Statistics Lesson Plans page on the Manga High website in a new tab.
Scroll down the page until you see the Find the Quartile and Interquartile Range activity and click on the orange arrow to complete the quiz.

Image link to Manga High website, Statistics activity page

Activity 3 - Minute to win it

Collect data by playing the Pom Pom/Cotton Ball minute to win it game and then use this data to find the mean, median, mode, range, quartiles and interquartile range.

Game instructions

You will need:

cotton balls or pom poms
a spoon
2 bowls
material for a blindfold such as a towel or scarf.

Note: You will need to be sitting down for this game.

Place the cotton balls into a bowl and place the bowl in your lap.
Wrap the blindfold around your eyes and head.
Grab the second bowl with one hand and hold it on top of your head.
Use your other hand to scoop with the spoon as many cotton balls as possible from the bowl in your lap to the one balanced on your head in 1 minute.
You will need a second person to watch and time you.
Record the number of cotton balls after each attempt. Do this activity at least 10 times to have enough data to analyse.

Materials for Pom Pom/Cotton Ball Minute to Win game, a bowl with cotton balls inside, a teaspoon, scarf and an empty bowl.

Minute to Win it Cotton Ball Challenge

Duration: 1:30

Task 1

Record your results as separate numbers in your exercise book or folder.
Use this data to find the mean, median, mode, range, quartiles and interquartile range.
Show all your working.

Activities too easy?

Click on the button to open the Mean, median, mode and range activity sheet and then use the template button to create a copy of the document.

Mean, median, mode and range activity sheet

Handing in your work

Don't forget to hand in the work you completed today!

Your teacher will have told you to do one of the following:
- Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
- Email any digital documents you created and any photos you took of your written work to your teacher.

Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.

Student reflection

Show how you feel about today's learning.

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