Teach GCSE Maths

x

x

x

x

x

xx

xx x

Weekly Household Income (£)f

(millions)

weekly household income (£)

Data Data HandlinHandlingg

The pages that follow are sample slides from the 30 presentations that cover the work for Data Handling.

The animations pause after each piece of text. To continue, either click the left mouse button, press the space bar or press the forward arrow key on the keyboard.

A Microsoft WORD file, giving more information, is included in the folder.

Animations will not work correctly unless Powerpoint 2002 or later is used.

F1: The 3 Ms and Range

The following extract comes from the 1st foundation presentation. Here the students are shown the importance of ordering the data when finding the median.

14 4

Can you find the medians of these data sets?

4 6 10 14 16

ANS: The numbers in the 2 sets are the same so the medians are both 10.

The median is only in the centre of the list if the data are in order.

Set A

106 16

6 14 4 10 16

Set B

median = 10

F9: Reading Stem and Leaf Diagrams

The work on stem and leaf diagrams gives an opportunity to revise the method of finding the median. This is shown on the next slide.

Key: 6 2 means 62 mm

Rainfall data

1098

7

317

765 6

02

50

7

Remind your partner how to find the median of a data set. Can you find the median here?

e.g The diagram shows the average rainfall (mm) for Newton Rigg ( UK ) from 1971 – 2000 for Jan. to Nov.

3

Ans: Median rainfall is 73 mm

The numbers are in order and there are 11 of them, so the median is the 6th.

1 2 3

4

5 6

Tip: Check there are the same number of numbers before and after the median. (Here there are 5 before

and 5 after)

Adapted from Crown copyright data supplied by the Met Office

F12: Histograms – Equal Class Widths

A short summary is provided in each presentation in a form suitable for note-taking. The next slide shows the summary for the introductory work on histograms.

frequency density

SUMMARY Frequencies on a histogram are shown by

area. E.g.

We plot frequency density on the y-axis.• Frequency density is found by

dividing each frequency by the class width.

frequency= 10 8 = 80

10

8

F14: Two-Way Tables

In addition to the questions asked of students as the theory is being developed, there are short exercises to check that the main points have been understood.

The icon in the top right hand corner indicates that in this exercise a calculator is not required.

Number of Computers

Number of

People

Exercise

1. The two-way table shows how the number of computers in a sample of 100 households is related to the number of people in the household.

0 1 2 3 4

1 4 4 1 1 0

2 3 3 1 1

3 1 3 3 5 0

4 1 1 3 0 2

5 0 3 2 1 1

(a) What does the 6 in the table tell us?

(c) Find the mean number of computers per household.

(b) How many households had more computers than the number of people?

6

Exercise

(a) There are 6 households with 2 people and 1 computer.

Number of Computers

Number of

People

3

1

3

6

4

1

1

0

5

1

1

3

0313

1332

2314

1205

0141

420

(b) There are 4 households with more computers than people.

Solution:

ExerciseSolutio

n:

total number of computers total number of households

The mean number of computers per household

=

= 1·62

Number of Computers

Number of

People

7112305

4

2

0

1

0

4

17

1

3

6

4

1

8

0

5

1

1

3

12313

14332

7314

50129Tota

l

10141

Total20

4 4 = 16

8150=

Total number of computers

= 81

0 9 = 01 17

= 172 12= 243 8 = 24

H3: Box Plots

As well as showing students how to draw box plots, the presentation on box plots uses real data to illustrate the usefulness of the diagrams when comparing data.

Rainfall in UK

Rainfall in France

Box and whisker diagrams are very useful for comparing data sets.

• The median rainfall was higher in France.

e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:

Rainfall in UK

Rainfall in France

• The range of rainfall amounts is greater in the U.K. . . .

Box and whisker diagrams are very useful for comparing data sets.

e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:

Rainfall in UK

Rainfall in France

but the interquartile range ( giving the middle 50% of amounts ) is greater in France.

• The range of rainfall amounts is greater in the U.K. . . .

Box and whisker diagrams are very useful for comparing data sets.

e.g. The following diagrams represent the rainfall in the first 16 days of March 2004 in 20 regions of the UK and of France:

H6: Probability and Independent Events

It is important for students to recognise the difference between independent events and those that are not independent. The presentation gives examples of situations involving both types.

, so multiplying the probabilities does not give the correct answer.

It’s starting to look as though we can always multiply probabilities of separate events to get the probability of both.

However, this isn’t true.

e.g. If I pick one of the following cards at random, what is the probability that it is pink and has a square on it?

Can you see the answer directly ?

Ans: p = 14However, the probability of pink =

14

and the probability of a square =

24

The next 2 slides contain a list of the 30 files that make up Data Handling.

The files have been labelled as follows:F: Topics for the Foundation level.H: Topics which appear only in the Higher level content.

Also for ease of access, colours have been used to group topics. For example, blue is used at both levels for work on probability.

The 2 underlined titles contain links to the complete files that are included in this sample.

F1 3 Ms and Range

F3 Frequencies and the MeanF4 Grouped Data and the Mean

F7 Reading Pie ChartsF8 Drawing Pie Charts

F19Collecting Data

F12Histograms – Equal Class Intervals

F13Scatter Graphs

F16Calculating Probabilities

F5 Discrete and Continuous DataF6 Pictograms, Bar Charts and Line Graphs

F21Index Numbers

F2 More About the Three Ms

Teach GCSE Maths – Data Handling

F17Probability - Theory and Experiment

F14Two Way Tables

F18 Sample Spaces

F20Questionnaires

F9 Reading Stem and Leaf Diagrams

F11Frequency Diagrams

F10Drawing Stem and Leaf Diagrams

Foundation

F15Introduction to Probability

continuedPage 1

H1 Cumulative Frequency Diagrams

H3 Box PlotsH4 Histograms – Unequal Class

Widths

H7 Tree DiagramsH8 Two-Way Tables and Probability

H5 Time Series and Moving AveragesH6 Probability and Independent Events

H2 Using Cumulative Frequency Diagrams

H9 Sampling Methods

Page 2

HigherTeach GCSE Maths – Data

Handling