handling data for gcse

7/30/2019 Handling Data for GCSE

1/44

Steve Bishop

First edition December 2012


2/44

Contents

Handling data checklist ............................................................................................ 3Handling data 1 ........................................................................................................... 4

The handling data cycle: .......................................................................................... 4Types of data ........................................................................................................... 4Collecting data ......................................................................................................... 5Displaying the data .................................................................................................. 6

Pictogram ............................................................................................................. 6Bar Chart .............................................................................................................. 7

Why are the following diagrams misleading? .......................................................... 9How to draw pie charts .......................................................................................... 10Stem and leaf diagrams ......................................................................................... 11

Handling data 2 ......................................................................................................... 14Mean, median and mode ....................................................................................... 14

Using frequency tables .......................................................................................... 16Grouped frequency tables ..................................................................................... 18Box and whisker diagrams .................................................................................... 20

Handling data 3 ......................................................................................................... 23Scatterplots ............................................................................................................ 23Correlation ............................................................................................................. 24Lines of best fit ...................................................................................................... 26Frequency polygons .............................................................................................. 29Two-way tables ...................................................................................................... 32Handling data 1 practice questions ....................................................................... 35Handling data 2 practice questions ....................................................................... 40

Mean, median, mode and range ........................................................................ 40mean from tables ............................................................................................... 42mean from grouped data .................................................................................... 43Box and whisker plots ........................................................................................ 44


3/44

Handling data checklist

Can do Help!Can'tdo

Tick the appropriate box

FCalculate the mode from a list of data

Calculate the range from a list of data

Collect & sort discrete data into a frequency table

Draw a simple line graph (such as temperature)

E

Calculate the mean from a list of data

Calculate the median from a list of data

Choose the best average to use & explain your decision

Interpret a line graph & bar chart

D

Calculate the averages from a frequency table

Distinguish between qualitative, quantitative, discrete & continuousdata

Collect & sort continuous data into groups within a frequency table

Draw a stem & leaf diagram

Draw a pie chart (by calculating the angles)

Draw a frequency polygon (it is a line graph for continuous data)

Plot a scatter graph & the line of best fit

Draw a histogram (it is a bar chart for grouped data)

Interpret a stem & leaf diagram

Interpret a pie chart (by using the angles)Interpret a frequency polygon (it is a line graph for continuous data)

Interpret a histogram (it is a bar chart for grouped data)

C

Calculate the averages from a grouped frequency table

Design a questionnaire & correct any deficiencies

Write a hypothesis & design a way of testing it

Compare data using all the averages

Describe correlation & use the line of best fit


4/44

Key words

DiscreteContinuousStem and leaf diagram

StemplotDataPictogramPie chart

Bar chartTallyFrequency

Handling data 1

The handling data cycle:

Types of data

Statistics is a branch of mathematics that is concerned with the collection, representationand interpretation ofdata.

There are different types of data:

Now try these 1State whether each of the following is qualitative orquantitative data. If quantitative, state

whether it is discrete orcontinuous.

(a) The number of pupils in a class.(b) The colour of cars in a car park.(c) The time spent by a motorist waiting at

a red traffic light.(d) The styles of womens dressesavailable in a chain store.

(e) The number of votes received by thecandidates in an election.

(f) The club of each of the members of theEngland football team.(g) The number of players from a club who

play football for England.(h) The mass of a new born baby.(i) The number of words on a page of a

book.(j) The duration of a hockey match.

Data

QuantitativeQualitative

Continuous

measuredDiscrete

counted


5/44

Page 5

Collecting data

Name Transport Time (mins)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Transport Tally Frequency


6/44

Page 6

Displaying the data

Pictogram

A pictogram is a very simple-to-read way of presenting data. It is cheerful and it makes apowerful visual impact.

Example

Population of Great BritainExcluding Ireland (figures in millions)

EACH FACE REPRESENTS 1 MILLION PEOPLE1801 (10.5) 1851 (21.0) 1901 (37.0)

But it is not very accurate (how would you draw 0.1 of a face?), and it can be ratherlaborious if you are drawing by hand.

Now try this 2

Draw a pictogram to represent the way in which students in your class have travelled tocollege


7/44

Page 7

Bar Chart

The bar chart is easier to draw than a pictogram and allows for greater accuracy. It is best

drawn on graph paper.Lets say that we have recorded the colours of the shirts of 30 students in a class, with the

following results (this is qualitative data):

RED 15 GREEN 5 BLUE 5 BLACK 3 WHITE 2

This can be presented in a frequency diagram with the bars either VERTICAL or

HORIZONTAL.

Note: 1. If the data are continuous, the bars should be next to each other.If the data are discrete or qualitative, the bars should be kept separate.

2. Each bar must be of exactly the same width.

3. The frequency scale must go up evenly and must start at 0.4. Everything should be clearly labelled.5. The bar can be plain, shaded or coloured.

Now try this 3Draw a bar chart to represent the way in which students in your class have travelled to

college

0

2

4

6

8

10

12

14

16

F

requency

Shirt Colour

0 2 4 6 8 10 12 14 16

Red

Green

Blue

Black

White

Frequency

Shirtc

olour


8/44

Page 8

Points 2 and 3 above are very important: you are not allowed to mislead the viewer bytampering with the scales and the bar widths.

For example, say there was a by-election and the result was:LABOUR 19,800CONSERVATIVE 14,500LIB. DEM. 13,000GREEN 11,000

Now look at this chart presenting the result:

A first glance suggests

that Labour has 4 or 5times as many votes asConservative and thatConservative has twice

as many as Lib. Dem.This is because we havemade the Labour bar look

bigger by making it wider.And, because we havestarted our scale at 10,000

votes, the Conservatives14,000 looks twice as large

as the Lib. Dem.s 12,000.THIS IS NOT ALLOWED!


9/44

Page 9

Why are the following diagrams misleading?

(a) (b)

Calcium

Sales Milk DRINK MILK

ITS BETTER 4U

Other drinks

1985 1986 1987 1990 1991

(c) (d) caloriesProfits

Coke Typicalother

` drink

Milk1987 1988 1989 1990 k

(e) (f)Sales Cost of a car

Price increases are slowing down!

Sales take off

All diagrams should:

be clearly labelled and titled

have the scales clearly identified

have the frequency begin at zero

have the units given

have the scales going up in equal amounts.


10/44

Page 10

How to draw pie charts

Step 1Put the information in a table

Eye colour No of people

Blue 5

Green 2

Hazel 2

Grey 1

Total 10

Step 2Work out how many degrees for one item360 represent 10 people

So 360 10 = 3636 represent 1 person

Step 3Write down in the table how many degrees for each item.

Eye colour No of people No of degrees

Blue 5 5 x 36 = 180

Green 2 2 x 36 = 72

Hazel 2 2 x 36 = 72

Grey 1 1 x 36 = 36

Total 10 360

Step 4Draw a circle and draw on the correct angles

Step 6Label the segments Grey

Eyes

Blue eyes

Hazel eyes

Green eyes

Now try this 4Draw a pie chart to represent the way in which students in your class have travelled to

college

If correct they should add up to 360


11/44

Page 11

Stem and leaf diagrams

Stem and leaf diagrams are also known as stemplots. They are useful ways of displayinginformation.

ExampleThese are the results for a module test for 10 students:

12 23 34 35 37 55 56 57 68 68

We can display this on a stem and leaf diagram.L = 12

1 2

2 33 4 5 7

45 5 6 7

6 8 8

H = 68n = 103 4 represents 34 marks

There are a number of basic elements to a stempot: stem, level, leaves.

L = 12

1 22 3

3 4 5 745 5 6 76 8 8

H = 71

n = 10 30 3 represents 33 marks

L indicates the lowest value and H the highest value.(The difference between H and L is the range)

Note that at each level the leaves are ordered, increasing as it moves away from the stem.

This makes it easier to find the middle (median) value.Note also that repeated data values (here 68) are recorded separately.

This column is the stem

This is the 20 level

7 is a leafon the 50 level: indicating the data value 57

This indicates the total number of dataitems

This is a key, which enables you to translate the level andleaf into a data value


12/44

Page 12

Now try this 5

Complete the stem and leaf plot for the following data

10 11 12 14 21 22 24 45 45 47 48 55 56

L =

1

2

3

4

5

H =n = 1 1 represents 11

Using stem and leaf plots to compare data higher tier

A stem and leaf plot helps us to compare visually two different but related data sets.

To do this we need to construct a back-to-back stem and leaf plot.

Example

In a module 2 test the same 10 students in a previous example scored the following results

25 33 40 42 43 45 56 57 57 69

Add this data to the first stem and plot diagram (from the above example) to form a back toback stem plot.

1 25 2 33 3 4 5 7

5 3 2 0 4

7 7 6 5 5 6 79 6 8 8

2 3 represents 23 marks scoredn = 10 n = 10

The back to back stem and leaf plot uses onestem but has two sets ofleaves, one to the

right and one to the left.

Remember the leaves are ordered so that larger leaves are further away from the stem.


13/44

Page 13

By looking at the back-to-back stem and leaf plot we can see that the module 2 test wasprobably easier - or that the students were better prepared - as students scored bettermarks.Now try this 6 (Higher tier)

The table below gives the annual rates of inflation for 10 countries in 1992 and 1991.Complete the back-to-back stem and leaf plot and comment on your results.

Country 1992 % change 1991 % change

UK 4.1 8.9

Australia 1.5 6.9

Canada 1.6 3.9

France 2.9 3.4

Germany 4.0 2.8

Italy 6.1 6.5

Japan 2.2 3.3

Netherlands 4.1 2.8

Spain 5.5 6.6USA 2.6 5.7

Finished early?Look at Handling data 1 practice questions on page 35


14/44

Page 14

Key wordsMean

MedianModeRangeFrequency

Handling data 2

Mean, median and mode

There are three types of average: mean, mode and median.

ModeThis is the one that occurs the most.

MedianThis is the one in the middle, when all the numbers have been put into numerical order.

MeanThis is the one that we normally think of when we are asked to find the average.

Mean = Total of the scoresNo of scores

This can be expressed mathematically asn

x

x

=

_

Where_

x represents the mean ofx, x represents the sum of all thexs and n is thenumber of values.

Range

The range is also an important piece of information. It tells us how spread out the

information is.Range = largest smallest

Example

Here are the scores that 5 people get for a test.

6 7 5 6 6

Find (a) the mean (b) the mode and (c) the median score and (d) the range

(a) Mean = 6 + 7 + 5 + 6 + 6 = 30 = 65 5

(b) Mode: 6 occurs the most (3 times) so the mode is 6

(c) Median

Step 1: put in numerical order: 5, 6, 6, 6, 7

Step 2: identify the middle number: 5, 6, 6, 6, 7So the median is 6.

(d) The range is 7 5 = 2.


15/44

Page 15

Now try these 71. Five other people take the same test and their scores are:

5 3 5 5 7

Find (a) the mean (b) the mode (c) the median score and (d) the range

2. The following are the midday temperatures over a week:

23 C 24C 25C 26C 20C 23C 27C

Find (a) the mean (b) the mode (c) the median score and (d) the range

3. Find the mean of these numbers:

200 400 200 100 100

Add five to each of the numbers now find the mean:

205 405 205 105 105

Subtract 10 from each of the original numbers and find the mean:

190 390 190 90 90

Add 23 to each of the original numbers. Can you find the mean without doing a calculation?

Multiply the original numbers by 2 and find the mean.

400 800 400 200 200

What do you notice?

The mean can be affected by extreme values; the median is not.


16/44

Page 16

Using frequency tables

When we have a large number of values it is easier to put the data into a frequency table.For example, if we survey 120 houses and asked how many people under the age of 16lived in the house, we might get the following results:

No under 16 0 1 2 3 4 5 6

frequency 37 23 34 18 5 2 1

To find the range from this data we can see that the number of children ranged from 0 to 6,so the range would be 6 0 = 6.

To find the mode, we have to look for the highest frequency, here it is 37. So most houseshave 0 children, hence the mode is 0.

To find the meanis more complicated. We need to find the total number of children and the

total number of houses.

To find the total number of houses we need to add up all the frequencies = 120.

The best way to find the total number of children is to redraw the table vertically and add

another column:

No of children Frequency Children Houses

x f f x

0 37 37 0 = 0

1 23 23 1 = 23

2 34 683 18 54

4 5 20

5 2 10

6 1 6

Totals =f 120 =fx 181

The mean number of children per house would then be

51.1120

181==

x

fxchildren per house.

Now try these 8

1 .The number of children per family on a housing estate were recorded as follows:

No of children No of families

x f

0 12

1 15

2 5

3 2

4 1

Find (a) the range (b) the mode and (c) the mean number of children per family.


17/44

Page 17

2. An agricultural researcher counted the number of peas in a pod in a certain strain asfollows:

No of peas No of pods

3 54 5

5 20

6 35

7 25

8 10

Find (a) the range (b) the mode and (c) the mean number of peas in a pod.


18/44

Page 18

Grouped frequency tablesGrouped frequency tables are used when a lot of data has to be recorded.Example

Hours 0-400 400-800 800-1200 1200-1600 1600-2000

No ofbulbs

2 5 7 5 1

The problem that we have here is that we cannot multiply 2 0-400.

We dont know exactly the life in hours for each bulb. So, we have toestimate its lifespan, by taking the midpoint of the group and use this to

multiply the number of bulbs.

The best way to do this is to redraw the table vertically with some extracolumns:

Hours Midpoint No of bulbsx f fx

0-400

2

4000 += 200

2 400

400-800

2

800400 +600

5 3000

800-1200 1000 7 7000

1200-1600 1400 5 7000

1600-2000 1800 1 1800

Totals =f 20 =fx 19200

==

20

19200

f

fx960 hours

To find the midpointadd the first and last

value and divide by 2:

2

4000+= 200


19/44

Page 19

Now try these 91. Andrew did a survey at the seaside for his science coursework.He measured the lengths of 55 pieces of seaweed.The results of the survey are shown in the table.

Length of seaweed(L cm)

Frequency

0 < L 20 2

20 < L 40 22

40 < L 60 13

60 < L 80 10

80 < L 100 5

100 < L 120 2

120 < L 140 1

Andrew needs to calculate an estimate for the mean length of the pieces of seaweed.Work out an estimate for the mean length of the piece of seaweed.

2. A set of 25 times in seconds is recorded.

12.9 10 4.2 16 5.6 18.1 8.3 14 11.5 21.7

22.2 6 13.6 3.1 11.5 10.8 15.7 3.7 9.4 8

6.4 17 7.3 12.8 13.5

(a) Complete the frequency table below, using intervals of 5 seconds.

Time (t) seconds Tally Frequency

0 t< 5

(b) Write down the modal class interval.

(c) Calculate the mean time.


20/44

Page 20

Box and whisker diagrams

A box and whisker diagram (sometimes called a boxplot) is another way of displaying thesame data that we find on a cumulative frequency curve.

To draw a box and whisker diagram you need the following information:

lowest value

lower quartilemedianupper quartilehighest value

This information is then drawn on a diagram as follows:

Lowest value Median Highest value

Lower quartile Upper quartile

Scale

ExampleThe midday temperature (in C) for 11 cities around the world are:

13 12 5 34 8 10 11 4 25 23 36

Draw a boxplot to illustrate this data.

First, put the data into order and then locate the median, LQ and UQ

4 5 8 10 11 12 13 23 25 34 36

LQ Median UQ

These values are then used to draw the boxplot

0 5 10 15 20 25 30 35 40


21/44

Page 21

Now try these 10

1. The following boxplot shows the class scores on a GCSE Maths mock paper

0 10 20 30 40 50 60

Find:

the median markthe lower quartile

the upper quartilethe inter-quartile rangethe highest markthe lowest mark

the range of the marks

2. (a) The following are the shoe size of eleven children:1 6 2 5 5 6 4 1 4 3 3

Draw a boxplot to illustrate the data using the scale below:

0 1 2 3 4 5 6

(b) The following are the times in minutes taken to evacuate a building over 15 different firetests:

5 6 6 5 6 4 7 88 8 4 6 7 7 5

Draw a boxplot to illustrate the data. (Draw your own scale)


22/44

Page 22

Now try these 11The stem and leaf diagram shows the ages of students in a maths group.L =

010 6 7 7 8 8 9 9 9 920 1 1 4 530 2405060 6

H =n =

How many students are there in the class?How old is the oldest student?How old is the youngest student?

What is the range?What is the modal age?What is the median age?

Find the mean age.

Draw a box plot to illustrate the data.

Finished early?Can you find 4 numbers that have a mode of 1, a median of 2 and a mean of 3?

Now have a look at Handling data sheet 2 on page 40


23/44

Page 23

Key wordsScatterplot

Scatter diagramScattergraphVariable

Correlation

Handling data 3

Scatterplots

Scatterplots (sometimes called scattergraphs, scattergrams or

scatter diagrams) are ways of displaying two variables. They can beused to see if there is some link between the two sets of data.

Match each person to the correct number on the scattergraph

Example

A survey was carried out by a group of students in which the height and weight of eachstudent was measured. The results were recorded in pairs (e.g. the student with height164cm weighed 58.2kg).

Height (cm) 164 152 173 158 177 173 179 168

Mass (kg) 58.2 50.8 60.3 56.0 76.2 64.2 68.8 60.5

In order to display this data on a scatter graph, two axes are drawn, one for the heights andone for the weights.

(It does not really matter which is which, but, as a general rule, the first set of data isrecorded along the horizontal axis and the second along the vertical axis).

Each point is plotted using the paired data as the co-ordinates, i.e. for the student with height164cm and weight 58.2 kg, the co-ordinates are (164, 58.2).

Scatter graph showing height/mass of students

40

50

60

70

80

140 145 150 155 160 165 170 175 180

height/ cm

mass/kg


24/44

Page 24

CorrelationLooking at the scatterplot above we can see that there is a link between a persons heightand their weight. In general the taller someone is the heavier they weigh. If there is a linkwe say that there is a correlation.There are three types of correlation: positive, zero and negative.

Positive Zero Negative

Positive

When there is a positive correlation as thexvalue increases so too does the yvalue.An example of positive correlation might be the number of police cameras and the number ofspeeding convictions; or height and foot size; or the amount of time spent revising and themarks in a maths exam.

ZeroZero correlation shows that there may well not be a link or relationship between the twovariables. For example, IQ and height, or the amount of food eaten and the marks on amaths exam.

NegativeIf the yvalue decreases as thexvalue increases then it has a negative correlation. An

examples of a negative correlation might be the age of a computer and its value; or theamount of time spent watching TV and the marks in maths coursework.

Strong, moderate and weak correlation

The correlation can also be strong, moderate or weak. The diagrams below give examplesof each for a negative correlation:

Strong Moderate Weak


25/44

Page 25

Now try these 12

1. The diagram shows three different types of scatter graphs.

Describe each of the different kinds of correlation.

The diagrams represent these three situations:

(a) the age of cars plotted against their value.

(b) the number of rooms in a house plotted against the value of the house.

(c) the age of adults plotted against their weight.

Which diagrams represent each of the situations?

2. For each of the following decide if there is a correlation and what sort of correlation itmight be:

(a) Number of people in a lift and the weight of the lift

(b) Shoe size of students and the number of brothers and sisters they have

(c) Marks in maths test and marks in a science test

(d) Speed of a car and the time it takes to stop

(e) Speed of a car and the time taken to travel 10 km

(f) Temperature of the room and the time taken for an ice cube to melt

(g) The height of a student and the time taken to do maths homework

(h) The time taken to revise for a test and the test results


26/44

Page 26

Now try these 13

Draw scatter graphs for the following data. State the type of correlation (none, positive,negative) and give some indication of the degree of correlation (strong, moderate, weak).

(a)

Mark on module 1: 15 20 14 5 24 10

Mark on module 2: 22 34 50 20 66 32

(b)

Age (years) 2 5 10 4 8 9

Price of car () 3250 1500 220 2400 1200 900

(c)

Shoe size 5 9 7 6 5 10Handspan 17 21 20 20 18 22

Lines of best fit

If the relationship between the two variables is linear (i.e. a straight line), then a line of bestfitcan be drawn.

This is done by drawing a line that goes through as many points as possible, with roughlythe same number above as below the line.

ExampleA class sat two maths tests on one algebra and another on handling data. The results areshown below:

Algebra Handling data

67 52

76 56

78 72

93 84

65 4361 78

56 67

38 34

54 62

72 77

84 84

To draw the line of best fit we must first plot the data on a scattergraph and then draw the

line of best fit by eye.


27/44

Page 27

We can then use the line of best fit to predict someones score in one paper if we know thescore in another.

For example, if a student scored 80 in the Algebra, what would the score be for Handlingdata?

Go to the 80 on the algebra axis go up until it hits the line and read off the correspondingHandling data value (75 marks).

Now try these 14

1. The scatter graph shows the height and mass of students. Draw a line of best fit on thegraph. Use the line of best fit to estimate the height of someone who has a mass of 60 kg.


28/44

Page 28

Whats happening here?What type of correlation is it?Does it mean that the more lemons that are imported the fewer road fatalities?


29/44

Page 29

Frequency polygons

Ungrouped data

ExampleThe results of a survey of 100 households are given in the table.

Number of people inhousehold

1 2 3 4 5 6

Frequency 11 28 21 25 10 5

Draw a frequency polygon to represent these data.

Now try this 15

1. The frequency distribution of the heights of some students is shownHeight (cm) 130- 140- 150- 160- 170- NB 140- means 140

Frequency 1 6 13 10 2 or more but lessthan 150

Draw a frequency polygon to illustrate the data.

0

5

10

15

2025

30

0 1 2 3 4 5 6 7

frequency

no. of people in household

Frequency Polygon to show no. of people in household


30/44

Page 30

Grouped dataSimilarly, for grouped data, the frequencies are plotted against the mid-pointof the classinterval and the points are joined with straight lines.

ExampleThe following table shows the heights of 65 people grouped into class intervals.

Height (cm) 150


31/44

Page 31

Example

The mock examinations results in Mathematics for two GCSE groups in two successiveyears are recorded on the table below.

Mark 1-20 21-40 41-60 61-80 81-100Group 1 (% frequency) 5 12 35 28 20Group 2 (% frequency) 7 26 48 9 10

i) Draw the frequency polygon for each group.ii) Comment on the mock examination papers, assuming that the ability of the

pupils was the same in each group.

Solution(i) In this example, in order to draw the frequency polygon, the percentage frequenciescould be plotted against the class mid-points, which are:

10.5, 30.5, 50.5, 70.5 and 90.5. It is not really necessary to plot the points to such a high

degree of accuracy so the values 10, 30, 50, 70 and 90 can be used.

(ii) Group 2 appear to have been given a more difficult examination paper than Group 1because a smaller number of people in group 2 obtained high marks in the examination.

[The average mark in group 2 was lower than in group 1]

Now try these 16

2. A teacher noted the absence rates of her maths class on Mondays and Fridays.The results are given on the table below.

No absent 0 1 2 3 4 5 6 7 8 9 10

from classMonday 3 6 6 7 4 4 3 0 0 0 0FrequencyFriday 0 2 2 3 4 6 3 0 7 3 2

Frequency

(i) Draw the frequency polygon for each day, using the same axes.(ii) Comment on the absence rates of the two days.

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70 80 90 100

Frequen

cy

Mark

Group

1

Group

2


32/44

Page 32

Two-way tablesCompleting two way tables

This is a typical (incomplete) two-way table.

How many people buy 100 g tea bags?How many buy 100g packet tea?The table is part of a GCSE question. It reads:

Bob carried out a survey of 100 people who buy tea.He asked them about the tea they buy most.The two-way table gives some information about his results.Complete the two-way table.

To complete the table we have to look at rows and columns that only have onemissing figure.Look at the first column.How many people in total have tea bags: 2 + 35 + 15 = 52Look at the second column.How many have 200 g packet tea?

25 (in total) (20 + 0) = 5.We can now complete some of the table:

Looking at the first row we can now find out how many in total use 50 g tea:2 + 0 + 5 = 7Looking at the second row we can find out how many have 100g tea:60 (35 + 20)= 60 55 = 5Adding these we get:

52

5


33/44

Page 33

We can now find the missing total in the end column100 (60 + 7) = 33

And the missing total in the bottom row:100 (52 + 25) = 23

This only leaves the 200 g instant tea figure to find.

We can do this in two ways a good way to check the figures:From the column: 23 (5 + 5) =13From the row: 33 (15 + 5) = 13

The answers agree.

The completed table will then look like:

52

5

5

7

52

7

5

5 33

23

13


34/44

Page 34

Now try these1.

How many males went to France?How many Males went to Spain?How many Males were there in total?

Complete the two-way table.

2.

Complete the two-way table.


35/44

Page 35

Handling data 1 practice questions

1.

2.


36/44

Page 36

3.


37/44

Page 37

4.

5.


38/44

Page 38

6.


39/44

Page 39

7.

8.


40/44

Page 40

Handling data 2 practice questions

Mean, median, mode and range


41/44

Page 41


42/44

Page 42

mean from tables

1.

2.

3.


43/44

Page 43

mean from grouped data


44/44

Box and whisker plots

handling data for gcse

Documents