1)   Mode, median, mean and range

2)   Pictograms

3)   Bar-charts

4)   Bar-graphs

5)   Tally charts

6)   Grouped Data and bar charts

7)   Frequency polygons

8)   Data in Tables

9)   Pie charts

 

SUMMARY OF WORK COVERED SO FAR

Mode, Median and Range

Aim:

To find the mode, median and range, and the modal class for grouped data.

Put these numbers in numerical order with the smallest first. 7, 3, 9, 2, 10, 8, 5, 4, 14, 12

2, 3, 4, 5, 7, 8, 9, 10, 12, 14,

34, 67, 38, 19, 44, 57, 24, 31, 62, 20

19, 20, 24, 31, 34, 38, 44, 57, 62, 67

2, -3, 1, 4, -4, 0, 5, -2

-5

1-4 -3 -2 0 2 4 5

-4 -3 -2 -1 0 2 3 4 51

Averages(mean)An average is a useful statistic because it represents a whole set of values by just a single or typical value.

• Where have you heard the word average before?

• Where have you seen it used?

The Mode

• The mode is a type of average

• The mode is the value that occurs most often in a set of data

Example5, 6, 8, 2, 4, 5, 3, 5 MODE = 5

Sometimes there is no mode because either all the values are different, or no single value occurs more often than other values

• What letter does your first name begin with?

What is the mode first letter for a name in class 7Y2?

THE MODE DOESN’T HAVE TO BE A NUMBER

The Median

• The median is another type of average• The median is the middle value for a set of data

when the values are put in numerical order.

Example

6, 8, 3, 7, 5, 2, 4 in order 2, 3, 4, 5, 6, 7, 8

Median = 5For an odd number of values in data set, there is only one middle value.

This is the median.

What is the median test score for the following set of results?

5, 7, 7, 8, 10, 12, 14, 15

For an even number of values in a data set, there are two middle values.

The median is the value in the middle of these two values.

Median = 9

The Range

• The range is not an average.• The range of a set of data is the largest

value minus the smallest value.• It shows how the data is spread out.

A small range shows that the values in a set of data are similar in size

A large range shows that the values differ considerably

Find the range:What number month were you born in?

Range = Largest number – smallest number

Range =

What does this tell us about the birthdays of class 7Y2?

For example, January = 1, June = 6, and December = 12

Modal ClassFor grouped data such as the example below, we cannot find the mode.

Time (Mins.) Frequency

0-2 2

3-5 4

6-8 3

9-11 1

Instead, we find the MODAL CLASS. This is the group that occurs most often.

Modal class = 3-5

Why isn’t it possible to calculate an exact mode or median from grouped data?

Write down:

5 numbers with a mode of 7

7 numbers with a median of 3

7 numbers with a mode of 6 and a median of 12

7 numbers with a mode of 5, median of 8, and a range of 10

Pie Charts

Be able to construct a pie chart from a collection of data, using a

protractor.

Makes of car in a school car park

Make Cavalier Ford Rover Volvo

Frequency 3 2 4 1Construct a pie chart to show this information.

A full circle is 360o

There are a total of 3+2+4+1 = 10 cars

We use 36o to represent each car

360o

Work out the missing numbers on this number spider

÷ 30

÷ 12

÷ 24

÷ 20

÷ 10

÷ 15

÷ 90

÷ 4

360

12

30

15

18

36

24

4

90

Makes of car in a school car park

Make Cavalier Ford Rover Volvo

Frequency 3 2 4 1

Angle in pie chart

We use 36o to represent each car so the3 Cavaliers are represented by 3x36o = 108o

Work out the angle needed for each of the other models of car

3x36o

=108o

2x36o

=72o

4x36o

=144o

1x36o

=36o

Makes of car in a school car park

Make Cavalier Ford Rover Volvo

Angle 108o 72o 144o 36o

Mark the centre of the pie and draw the circle.

Draw a line from the centre to the edge

Measure the first angle needed (108o)

Draw in the line and label the section

108oCavalier

Makes of car in a school car park

Make Cavalier Ford Rover Volvo

Angle 108o 72o 144o 36o

From this line measure the next angle, draw the line and label the section.

Continue in this way

Check that the last section has the correct angle and label it.

72o

Cavalier

Ford144o

Rover

36oVolvo

Why?

• Why do we use 36o to represent 1 car?

• What would happen if there were 20 cars?

• What about 60 cars? Or 15 cars?

If there were 20 cars in your survey, what angle would you use to represent 4 cars? 7 cars? 12 cars?

Q1 A survey of how 30 pupils got to school

Q2 How Cameroon spent his £40 birthday money

Q3 Who is your favourite Telly-Tubby survey.

Construct Pie charts questions

Method Walk Cycle Car Bus

Frequency 15 5 7 3

How Games Clothes Books Cinema

Amount £6 £19 £9 £6

Telly-Tubby

Tinky-Winky

Dipsy La-La Po

Frequency 12 20 18 40

Interpreting Pie Charts20 pupils in class 3B travel to school. From the chart

find the number of pupils who travel by each method.

Walk =

Cycle =

Bus =

920360162

42036072

720360126

180 boys in year 5 chose their favourite sport. From the chart find how many chose each sport.

Football144°

Rugby80°

Cross Country

40°

Hockey60°

Squash36°

300 passengers boarded a train in London. From the chart find how many are travelling to each destination.

Southampton120°

Poole60°

Parkstone36°

Branksome54°

Bournemouth90°

150 packets of crisps were sold from a vending machine. From the chart find the number for each flavour. Find also the percentage for each.

Cheese & Onion60°

Prawn Cocktail36°

Salt & Vinegar72°

Plain144°

AnswersYear 7 pupils travel to school

Walk, 15, 50%

Cycle, 5, 17%

Car, 7, 23%

Bus, 3, 10%

How Cameron spent his birthday money

Games, £6, 15%

Clothes, £19, 47%

Books, £9, 23%

Cinema, £6, 15%

Favourite Telly-Tubby

Tinky-Winky, 12,

13%

Dipsy, 20, 22%

La-La, 18, 20%

Po, 40, 45%

Sports:Football: 72, Rugby 40, Hockey 30Cross Country 20, Squash 18 pupils.

Passengers: Southampton 100, Bournemouth 75, Poole 50, Branksome 45, Parkstone 30.

Crisps: Plain 60, Cheese & Onion 45,Salt & Vinegar 30, Prawn Cocktail 15