Unit 8 Section 1 : Data Collection, Extraction and Presentation

Example 1

The table gives the distances, in miles, between some towns and cities. Use this table to answer the questions below.

(a)

How far is it from Hull to Nottingham?

From the table, Hull to Nottingham is 73 miles.

(b)

Andy drives from Leicester to Lincoln and then on from Lincoln to Doncaster. How far does he drive altogether?

From the table,	Leicester to Lincoln is 51 miles
and	Lincoln to Doncaster is 39 miles.

Total distance	= 51 + 39
	= 90 miles

(c)

Ian drives from Hull to Sheffield and then back to Hull. How many miles, in total, does he drive?

From the table, Hull to Sheffield is 61 miles.

Total distance	= 61 × 2
	= 122 miles

Example 2

Use the following timetable to answer the questions below.

(a)

Alan catches the 2017 train at Cuffley. When does he arrive at Hornsey?

Alan arrives at 2042.

(b)

Julie arrives at Hornsey at 2212. When did she leave Palmers Green?

Julie left at 2206.

Example 3

A class of pupils take a test. Their scores are listed below:

17	23	46	31	17	19	26	31	42	5
21	32	36	37	32	38	41	40	19	12
7	48	29	39	42	38	41	32	36	35

Draw a stem and leaf diagram for this data.

In this stem and leaf diagram we treat the numbers of 10s as the stem and the numbers of units as the leaves.

In the following stem and leaf plot the data has not been put into order;

Stem	Leaf
0	5	7
1	7	7	9	9	2
2	3	6	1	9
3	1	1	2	6	7	7	8	9	8	2	6	5
4	6	2	1	0	8	2	1

The leaves can now be ordered as shown to produce the final diagram:

Stem	Leaf
0	5	7
1	2	7	7	9	9
2	1	3	6	9
3	1	1	2	2	5	6	6	7	7	8	8	9
4	0	1	1	2	2	6	8

Example 4

A student records the temperature in a greenhouse every 4 hours during 1 day. The results are listed below:

Time	0000	0400	0800	1200	1600	2000	2400
Temperature (°C)	6	5	9	21	25	12	8

Draw a line graph and use it to estimate the temperature at 1000 and 1400.

The line graph is shown below:

The dotted lines show how to estimate the temperatures at 1000 and 1400. These estimates are:

	15 °C at 1000
and	23 °C at 1400.

Example 5

Throughout a 4-week period a class recorded the number of children absent each day. Their results are listed below:

1	0	4	3	1	2	1	3	4	5
7	1	2	2	3	3	1	3	1	0

Collate this data using a tally chart and draw a vertical line graph to illustrate the data.

The tally chart is shown below:

Number of Children Absent	Tally	Frequency
0		2
1		6
2		3
3		5
4		2
5		1
6		0
7		1

The vertical line graph is shown below:

Example 6

These pie charts show some information about the ages of people in Greece and in Ireland. There are about 10 million people in Greece, and there are about 3.5 million people in Ireland.

(a)

Roughly what percentage of people in Greece are aged 40 - 59 ?

The angle for 40-59 is about 90°;

the fraction of the total is

, or 25%.

(b)

There are about 10 million people in Greece. Use your percentage from part (a) to work out roughly how many people in Greece are aged 40 - 59.

25% of Greece's population =

× 10 million = 2.5 million.

(c)

Dewi says that these charts show that there are more people under 15 in Ireland than in Greece.

Dewi is wrong. Explain why the charts do not show this.

This is not true; the percentage of people under 15 is higher in Ireland than in Greece, but Greece has a far larger population than Ireland. The actual numbers are:

Ireland :

× 3.5 million ≈ 0.875 million

Greece :

× 10 million =

× 10 million ≈ 1.67 million

(d)

There are about 60 million people in the UK. The table shows roughly what percentage of people in the UK are of different ages.

under 15	15-39	40-59	over 59
20%	35%	25%	20%

Copy and complete the pie chart below to show the information in the table. Label each section of your pie chart clearly with the ages.

Since there are 10 equal sectors in the pie chart, each sector is

= 36°,

and each sector represents 10% of the people in the UK.

Sectors are:

under 15

15-39

40-59

over 59

2 sectors

sectors

2 sectors

Exercises

Question 1

Use this mileage chart to answer the following questions:

(a)

How far is it from Hitchin to Royston?

miles

(b)

Alan drives from Bedford to Royston and then back again. How far does he travel in total?

miles

(c)

David cycles from Bedford to Hitchin, then from Hitchin to Royston and from Royston back to Bedford. How far does he cycle altogether?

miles

(d)

A lorry is driven from Cambridge to Northampton, then from Northampton to Hitchin and from Hitchin back to Cambridge. How far does the lorry travel altogether?

miles

(e)

Is the journey from Cambridge to Northampton shorter than the journey from Cambridge to Wellingborough?

No: Cambridge to Northampton is 50 miles and Cambridge to Wellingborough is only 44 miles.

Question 3

Use the following timetable to answer these questions:

(a)

Which train should you catch at Birmingham Moor Street to arrive in Wilmcote before 1700 ?

(b)

Nick arrives in Yardley Wood at 1603. At what time did he leave Jewellery Quarter?

(c)

Ali leaves Spring Road at 1534. At what time will he arrive at Earlswood?

(d)

Michaela arrives at Hall Green station at 1445. She wants to travel to Henley-in-Arden. What is the earliest time that she could arrive there?

(e)

Denise wants to travel from Bordesley to Yardley Wood. At what time must she leave Bordesley?

(f)

Johnny wants to travel from Small Heath to Earlswood. He arrives at Small Heath station at 1500. Describe how he can get to Earlswood.

Board the to , arriving at ;
then board the to , arriving .

Question 4

Use the following timetable to answer the questions below:

(a)

Jack catches the 0933 train from Manchester. At what time would he arrive in Weston-super-Mare?

(b)

Josh wants to travel to Camborne. What is the latest time that hecould leave Manchester Piccadilly?

(c)

Kate catches the 1026 at Stafford. At what time will she arrive in Torquay?

(d)

Hannah leaves Wolverhampton and arrives in Weston-super-Mare at 1522. At what time did she leave Wolverhampton?

(e)

Matthew leaves Taunton at 1405. At what time does he arrive in Penzance?

(f)

Serena catches the 1641 at St Austell. At what time does she arrive in St Erth?

Question 5

As part of a science project, the height of a plant is measured every 3 days. The readings are listed in the following table:

Day	0	3	6	9	12	15	18
Height(cm)	4	6	9	14	16	19	24

(a)

Draw a line graph to show how the height of the plant varies with time.

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(b)

Estimate the height of the plant after 14 days.

About cm

(c)

Estimate the age of the plant when the height was 8 cm.

About days

Question 6

Records were kept of the mass of a baby for the first few days of its life. The information is listed in the table below:

Day	0	2	4	6	8	10	12	14	16
Mass(kg)	3.7	3.6	3.3	3.5	3.7	3.8	4.0	4.2	4.3

(a)

Draw a line graph to show how the mass of the baby changes.

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(b)

Use the line graph to estimate the mass on:

(i)	day 1,	≈ kg
(ii)	day 7,	≈ kg
(iii)	day 15,	≈ kg

Question 7

Jane measured the height of her son, Chris, every two years and kept a record of the heights.

Chris' Age	1	3	5	7	9	11
Height (cm)	59	81	102	110	131	156

(a)

Draw a line graph using this data.

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(b)

Estimate Chris' height when he was:

(i)	2 years old,	≈ cm
(ii)	10 years old,	≈ cm

Question 8

The results of a maths test for one class are listed below:

42	31	29	38	24	17	9	18	28	27
34	35	38	40	40	19	32	39	22	11
11	9	2	17	32	19	22	29	31	33

Illustrate this data using an ordered stem and leaf diagram using stems of 0, 10, 20, 30 and 40.

Stem	Leaf
0
1
2
3
4

Question 9

The data collected in a survey on the number of children in each family is listed below:

2	3	1	2	1	2	3	1	2	6	1	2	3	3	4	1	5	2	3	2
1	3	1	2	4	5	2	2	2	3	1	1	3	1	1	2	2	3	4	2

(a)

Draw up a tally and frequency table for this data.

No. of Children	Tally	Frequency
0
1
2
3
4
5
6

(b)

Illustrate this data using a pictogram.

Click on a symbol to make it coloured. Click again to colour a part of it.

1 child		Each symbolrepresents 2 families
2 children
3 children
4 children
5 children
6 children

(c)

Illustrate this data using a vertical line graph.

Question 10

Data was collected on the amount, in pence, that children spent in a tuckshop in one session. This data is illustrated in the following stem and leaf diagram.

Stem	Leaf
20	7	7	8	8	8	9	9	9	9
30	0	0	0	0	1	2	2	2	5	5	5	6	6	8	8	9
40	0	0	1	1	1	2	3	3	3	4	4	5	5	5	7	7
50	0	0	0

Use a vertical line diagram to illustrate the data.

Question 12

A small cafe sells sandwiches, ice creams, hot drinks and cold drinks. The pictogram shows what they sold on Monday.

(a)

How many cold drinks did they sell?

(b)

How many ice creams did they sell?

(c)

How many hot drinks did they sell?

The pictogram below shows how many sandwiches and ice creams the cafe sold on Tuesday.

(d)

The cafe also sold 40 hot drinks on Tuesday. Show this number on the pictogram below.

(e)

The cafe also sold 12 cold drinks on Tuesday. Show this number of cold drinks on the pictogram you have drawn.

(f)

Look at both the pictograms. What can you tell about the weather on each day?

Tuesday was a day than Monday.

Since more ice creams and cold drinks were bought on Monday than on Tuesday, it is likely that Tuesday was a colder day than Monday.

Question 14

(a)

Lisa works in a shoe shop. She recorded the size of each pair of trainers that she sold during a week. This is what she wrote down:

Use a tallying method to make a table showing how many pairs of trainers of each size were sold during the whole week.

Size of Trainers	Tally	Total Sold During Week
4
5
6
7
8
9

(b)

Which size of trainer did Lisa sell most of?

Size

(c)

Lisa said that most of the trainers sold were bigger than size 6. Is Lisa right?

It can be told from the table:
Count up number sold of sizes 4, 5, 6 and compare with number sold of sizes 7, 8, 9.

Question 15

This chart shows the distances in miles between six towns.

Example: Cardiff and London are 152 miles apart.

(a)

How far apart are Cardiff and Newcastle?

miles

(b)

How far apart are London and Edinburgh?

miles

(c)

Which town is 198 miles from Cardiff?

(d)

Which two towns are exactly 300 miles apart?

(e)

Which town is the greatest distance from Plymouth?

(f)

Which town is the smallest distance from Cardiff?

(g)

Gwen is a lorry driver. She drove from London to Newcastle, then from Newcastle to Edinburgh. She filled in her job sheet.

From	To	Distance
London	Newcastle	280
Newcastle	Edinburgh	107

She drove back using the same route. Copy and complete her job sheet.

From	To	Distance
Edinburgh

Question 16

The two frequency diagrams below show the amount of rain that fell in two different months.

(a)

How many days are in month A?

days

Add up the bar heights from the first diagram: 10 + 8 + 6 + 5 + 1 = 30 days

(b)

Carl asks 5 friends how much rain fell during month A. They said:

Jon: 5 mm,

Dipta: 25 mm,

Ian: 30 mm,

Nerys: 75 mm,

Sue: 250 mm

Only one friend could have been right. You can tell who it is without trying to work out the total rainfall.

Which one of Carl's friends could have been right?

There are 5 days with 15 to 20 mm of rainfall, so these 5 days procedure more than 75 mm of rainfall, which makes all the other suggestions wrong.

(c)

Sudi said:

"The diagram for month B shows that it rained more at the end of the month."

Is Sudi right?

Sudi is wrong because the horizontal axis does not record the days of the month, merely the amount of rainfall, so you cannot tell which days in the month produced the high rainfall.

25	of the children are 4 years old.
20	of the children are 3 years old.
5	of the children are 2 years old.

F	P	F	B	P	Re	C	M	C	Re	F	V
Ro	Ro	Fi	F	Fi	Fi	B	P	C	Re	M	Re
F	Fi	M	Ro	F	F	F	P	Re	Ro	P	C
M	F	F	Re	Ro	C	Ro	F	M

(i) What time does it arrive in Colton?
(ii) How much time does the bus journey take?	minutes

F	P	F	B	P	Re	C	M	C	Re	F	V
Ro	Ro	Fi	F	Fi	Fi	B	P	C	Re	M	Re
F	Fi	M	Ro	F	F	F	P	Re	Ro	P	C
M	F	F	Re	Ro	C	Ro	F	M

F	P	F	B	P	Re	C	M	C	Re	F	V
Ro	Ro	Fi	F	Fi	Fi	B	P	C	Re	M	Re
F	Fi	M	Ro	F	F	F	P	Re	Ro	P	C
M	F	F	Re	Ro	C	Ro	F	M