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Haringey Sixth Form Mathematics Department 1

DATA HANDLING EXAM QUESTIONS

SHOW ALL YOUR WORKING OUT

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Questionnaires

1. The manager of a school canteen has made some changes.

She wants to find out what students think of these changes.

She uses this question on a questionnaire.

"What do you think of the changes in the canteen?"

Excellent Very good Good

(a) Write down what is wrong about this question.

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................ (1)

This is another question on the questionnaire.

"How much money do you normally spend in the canteen?"

A lot Not much

(b) Write down one thing that is wrong with this question.

........................................................................................................................................

........................................................................................................................................

........................................................................................................................................ (1)

(Total 2 marks)


2. Petros wants to find out how teenagers communicate with each other.

He designs a questionnaire.

Here are two of his questions.

The questions are not suitable.

For each question, write down a reason why.

(i) Do you prefer to communicate with your best friend by mobile phone or by e-mail?

Yes No

Reason..........................................................................................................................

.....................................................................................................................................

(ii) How many e-mail addresses do you have?

1 2 3 4

Reason..........................................................................................................................

..................................................................................................................................... (Total 2 marks)

Stem and leaf diagrams

3. Here are the times, in minutes, taken to change some tyres.

5 10 15 12 8 7 20 35 24 15

20 33 15 25 10 8 10 20 16 10

In the space below, draw a stem and leaf diagram to show these times.

(Total 3 marks)


4. A table tennis club has 180 members.

117 of the members are adults and the rest are children.

The ratio of the number of right-handed members to the number of left-handed

members is 11 : 1.

(a) How many of the 180 members are right-handed?

………………. (2)

Here are the ages in years of the members who won their matches in the cup

competition yesterday.

8 17 10 16 24 29 36 25 38 42

53 44 49 53 29 21 11 38 9 29

(b) In the space below draw a stem and leaf diagram to show these ages.

(3)

(Total 5 marks)

Probability

5. Four teams, City, Rovers, Town and United play a competition to win a cup. Only one team can

win the cup.

The table below shows the probabilities of City or Rovers or Town winning the cup.

City Rovers Town United

0.38 0.27 0.15 X

Work out the value of x.

......................... (Total 2 marks)


6. Mr Brown chooses one book from the library each week.

He chooses a crime novel or a horror story or a non-fiction book.

The probability that he chooses a horror story is 0.4

The probability that he chooses a non-fiction book is 0.15

Work out the probability that Mr Brown chooses a crime novel.

……………………. (Total 2 marks)

7. Twenty students took a short test.

The test was marked out of 5.

Their results are shown in the table below.

Mark 0 1 2 3 4 5

Number of Students 3 5 4 5 2

(a) Write down the probability that a student chosen at random scores 2 in the test.

……………. (1)

(b) Write down the probability that a student chosen at random scores 3 or more in the test.

……………… (2)

(Total 3 marks)


8. Tony throws a biased dice 100 times.

The table shows his results.

Score Frequency

1 12

2 13

3 17

4 10

5 18

6 30

He throws the dice once more.

(a) Find an estimate for the probability that he will get a 6.

..................................... (1)

Emma has a biased coin.

The probability that the biased coin will land on a head is 0.7

Emma is going to throw the coin 250 times.

(b) Work out an estimate for the number of times the coin will land on a head.

..................................... (2)

(Total 3 marks)

9. Kevin regularly travels from Manchester to Oxford.

He travels on two different trains.

His first train is from Manchester to Birmingham and his second train is from Birmingham to

Oxford.

On the 1st train, the probability that a seat has a table is 5

3.

On the 2nd train, the probability that a seat has a table is 10

3.

The 1st train has a total of 400 seats.

(a) Work out an estimate for the number of these 400 seats that have a table.

…………………… (2)


Kevin is travelling from Manchester to Oxford tomorrow.

(b) Complete the probability tree diagram to show the outcomes of Kevin’s seating on the two

trains.

Label clearly the branches of the probability tree diagram.

The probability tree diagram has been started in the space below.

Seat on the Seat on thefirst train second train

with atable

withouta table

35

(3)

(Total 5 marks)


Scatter graphs

10. The scatter graph shows information about 12 countries.

For each country, it shows the percentage of the population in farming jobs and the percentage

of the population living in towns.

80

70

60

50

40

3010 20 30 40 50 60 70 80

Percentage in farming jobs

Percentageliving intowns

×

×

×

×

×

×

×

×

×

××

×

(a) Describe the relationship between the percentage of the population in farming jobs and the

percentage of the population living in towns.

……………………………………………………………………………………………

…………………………………………………………………………………………… (1)

(b) Draw the line of best fit on the scatter graph. (1)

In Mathsland, the percentage of the population in farming jobs is 35%.

(c) Use your line of best fit to estimate the percentage of Mathsland’s population living in

towns.

……………………. % (1)

(Total 3 marks)


11. The table shows the number of pages and the weight, in grams, for each of 10 books.

Number of pages 80 130 100 140 115 90 160 140 105 150

Weight (g) 160 270 180 290 230 180 320 270 210 300

(a) Complete the scatter graph to show the information in the table.

The first 6 points in the table have been plotted for you. (1)

320

300

280

260

240

220

200

180

16060 80 100 120 140 160 180

Number of pages

Weightof book

(g)

×

× ×

×

×

×


(b) For these books, describe the relationship between the number of pages and the weight of

a book.

................................................................................................................................................

................................................................................................................................................ (1)

(c) Draw a line of best fit on the scatter diagram. (1)

(d) Use your line of best fit to estimate

(i) the number of pages in a book of weight 280 g,

................. pages

(ii) the weight of a book with 120 pages.

........................ g (2)

(Total 5 marks)

12. Pablo is an artist.

The scatter graph, below, gives information about the area and the cost of some of his pictures.

The table shows the area and the cost of another three of his pictures.

Area (cm2) 2000 2900 3260

Cost (£) 1150 1250 1500

(a) On the scatter garph, plot the information from the table. (1)

(b) Describe the relationship between the area of a picture and its cost.

................................................................................................................................................

................................................................................................................................................ (1)

(c) Draw a line of best fit on the scatter graph. (1)

(d) Use your line of best fit to find an estimate of the cost of a picture with an area of

2500 cm2.

£................................. (1)


All Pablo’s pictures are rectangles.

One of his pictures costs £1000.

Its length is 48 cm.

(e) Use your line of best fit to find an estimate for the width of the picture.

............................... cm (2)

1600

1400

1200

1000

800

600

400

200

00 500 1000 1500 2000 2500 3000

Area (cm )

Cost (£)

2

×

×

× ××××××

(Total 6 marks)


Cumulative frequency

13. The table shows information about the number of hours that 120 children used a computer last

week.

Number of hours

(h)

Frequency

0 < h ≤ 2 10

2 < h ≤ 4 15

4 < h ≤ 6 30

6 < h ≤ 8 35

8 < h ≤ 10 25

10 < h ≤ 12 5

(a) Complete the cumulative frequency table.

Number of hours

(h)

Cumulative

frequency

0 < h ≤ 2 10

0 < h ≤ 4

0 < h ≤ 6

0 < h ≤ 8

0 < h ≤ 10

0 < h ≤ 12

(1)


140

120

100

80

60

40

20

Cumulativefrequency

O 2 4 6 8 10 12Number of hours ( )h

(b) On the grid, draw a cumulative frequency graph for your table. (2)

(c) Use your graph to find an estimate for the number of children who used a computer for

less than 7 hours last week.

………………... (2)

(Total 5 marks)


14. Daniel took a sample of 100 pebbles from Tawny Beach.

He weighed each pebble and recorded its weight.

He used the information to draw the cumulative frequency graph shown on the grid.

(a) Use the cumulative frequency graph to find an estimate for

(i) the median weight of these pebbles,

.............................. grams

(ii) the number of pebbles with a weight more than 60 grams.

......................................... (3)

120

100

80

60

40

20

10 20 30 40 50 60 70 80

Weight (grams)

CumulativeFrequency

O


Daniel also took a sample of 100 pebbles from Golden Beach.

The table shows the distribution of the weights of the pebbles in the sample from Golden Beach.

Weight (w grams) Cumulative frequency

0 < w 20 1

0 < w 30 15

0 < w 40 36

0 < w 50 65

0 < w 60 84

0 < w 70 94

0 < w 80 100

(b) On the same grid, draw the cumulative frequency graph for the information shown in the

table. (2)

Daniel takes one pebble, at random, from his sample from Tawny Beach and one pebble, at

random, from his sample from Golden Beach.

(c) Work out the probability that the weight of the pebble from Tawny Beach is more than

60 grams and the weight of the pebble from Golden Beach is more than 60 grams.

..................................... (4)

(Total 9 marks)

Averages from tables

15. Fred did a survey on the areas of pictures in a newspaper.

The table gives information about the areas.

Area (A cm2) Frequency

0 < A 10 38

10 < A 25 36

25 < A 40 30

40 < A 60 46

Work out an estimate for the mean area of a picture.

.................................cm2

(Total 4 marks)


16. Bill recorded the times, in minutes, taken to complete his last 40 homeworks.

This table shows information about the times.

Time (t minutes) Frequency

20 ≤ t < 25 8

25 ≤ t < 30 3

30 ≤ t < 35 7

35 ≤ t < 40 7

40 ≤ t < 45 15

(a) Find the class interval in which the median lies.

..................................... (1)

(b) Calculate an estimate of the mean time it took Bill to complete each homework.

.....................................minutes (4)

(Total 5 marks)

17. Marcus collected some pebbles.

He weighed each pebble.

The grouped frequency table gives some information about weights.

Weight (w grams) Frequency

50 w < 60 5

60 w < 70 9

70 w < 80 22

80 w < 90 27

90 w < 100 17

Work out an estimate for the mean weight of the pebbles.

………………………… grams (Total 4 marks)


Sampling

18. 340 475 people live in Brinton.

A company carried out a survey.

It used a random sample of 1500 of the 340 475 people.

870 of this sample of 1500 people were male.

Work out an estimate for the number of females living in Brinton.

…………………. (Total 3 marks)

19. There are 800 pupils at Hightier School.

The table shows information about the pupils.

Year group Number of boys Number of girls

7 110 87

8 98 85

9 76 74

10 73 77

11 65 55

An inspector is carrying out a survey into pupil’s views about the school. She takes a sample,

stratified both by Year group and by gender, of 50 of the 800 pupils.

(a) Calculate the number of Year 9 boys to be sampled.

……………………. (2)

Toni stated “There will be twice as many Year 7 boys as Year 11 girls to be sampled.”

(b) Is Toni’s statement correct?

You must show how you reached your decision.

(2)

(Total 4 marks)


20. Charles found out the length of reign of each of 41 kings.

He used the information to complete the frequency table.

Length of reign

(L years) Number of kings

0 < L 10 14

10 < L 20 13

20 < L 30 8

30 < L 40 4

40 < L 50 2

(a) Write down the class interval that contains the median.

….……………………. (2)

(b) Calculate an estimate for the mean length of reign.

…………………. years (4)

(Total 6 marks)


DATA HANDLING EXAM QUESTIONS

NON CALCULATOR SECTION

Averages From Tables

21. Rosie had 10 boxes of drawing pins.

She counted the number of drawing pins in each box.

The table gives information about her results.

Number of

drawing pins Frequency

29 2

30 5

31 2

32 1

(a) Write down the modal number of drawing pins in a box.

................................. (1)

(b) Work out the range of the number of drawing pins in a box.

................................. (1)

(c) Work out the mean number of drawing pins in a box.

................................. (3)

(Total 5 marks)

22. There are 10 children in a playgroup.

The table shows information about the ages, in years, of these children.

Age in years Frequency

2 3

3 5

4 2

Work out the mean age of the children.

.................................. years (Total 3 marks)


23. 20 students scored goals for the school hockey team last month.

The table gives information about the number of goals they scored.

Goals scored Number of students

1 9

2 3

3 5

4 3

Work out the mean number of goals scored.

.......................... (Total 3 marks)

Cumulative Frequency

24. 30 students took part in a National Science quiz.

The quiz was in two parts.

The cumulative frequency graph on the grid below gives information about the marks scored in

Part One.

The lowest mark was 5 and the highest mark was 47.


30

20

10

10 20 30 40 50Marks

PART ONE

Cumulativefrequency

0

10 20 30 40 50Marks

0

PARTONE

10 20 30 40 50Marks

0

PARTTWO

(a) In the space provided on the grid, draw a box plot using the cumulative frequency graph

for the results of Part One. (3)


The diagram also shows a box plot for the results of Part Two.

Use the box plots to compare the two distributions.

(b) Give two differences between them.

First difference............................................................................................................

.....................................................................................................................................

Second difference........................................................................................................

..................................................................................................................................... (2)

(Total 5 marks)

25. 40 boys each completed a puzzle.

The cumulative frequency graph below gives information about the times it took them to

complete the puzzle.

(a) Use the graph to find an estimate for the median time

............... seconds (1)

Cumulativefrequency

40

30

20

10

10 20 30 40 50 60

Time in seconds

O

For the boys

the minimum time to complete the puzzle was 9 seconds

and the maximum time to complete the puzzle was 57 seconds.


(b) Use this information and the cumulative frequency graph to draw a box plot showing

information about the boy’s times.

0 10 20 30 40 50 60

Time in seconds (3)

The box plot below shows information about the times taken by 40 girls to complete the

same puzzle.

10 0 20 30 40 50 60

Time in seconds

(c) Make two comparisons between the boys’ times and the girls’ times.

...............................................................................................................................................

............................................................................................................................................... (2)

(Total 6 marks)

26. The table shows information about the heights of 40 bushes.

Height (h cm) Frequency

170 h < 175 5

175 h < 180 18

180 h < 185 12

185 h < 190 4

190 h < 195 1

(a) Complete the cumulative frequency table.

Height

(h cm)

Cumulative

Frequency

170 h < 175

170 h < 180

170 h < 185

170 h < 190

170 h < 195

(1)


(b) On the grid, draw a cumulative frequency graph for your table.

40

30

20

10

0170 175 180 185 190 195

Height ( cm)h

Cumulativefrequency

(2)

(c) Use the graph to find an estimate for the median height of the bushes.

……………………… cm (1)

(Total 4 marks)

27. The times, in seconds, taken by 11 teachers to solve a puzzle are listed in order

4 12 13 17 18 20 22 24 25 30 34

(a) Find

(i) the lower quartile,

………………………seconds

(ii) the interquartile range.

…………………………seconds (2)


(b) Draw a box plot for this data.

0 5 10 15 20 25 30 35

Time (seconds)

(3)

(Total 5 marks)

28. Mary recorded the heights, in centimetres, of the girls in her class.

She put the heights in order.

132 144 150 152 160 162 162 167

167 170 172 177 181 182 182

(a) Find

(i) the lower quartile,

........................... cm

(ii) the upper quartile.

........................... cm (2)

(b) On the grid, draw a box plot for this data.

130 140 150 160 170 180 190 cm

(3)

(Total 5 marks)


Probability

29. The table shows information about the number of fillings the students in a class had last year.

Number of

fillings

Number of

students

0 10

1 5

2 4

3 2

More than 3 1

The headteacher is to choose a student at random from the class.

Find the probability that she will choose a student who had

(a) exactly 1 filling,

………………… (1)

(b) 2 or more fillings,

………………… (1)

(c) either 1 filling or 2 fillings.

………………… (1)

(Total 3 marks)

30. The probability that a biased dice will land on a four is 0.2

Pam is going to roll the dice 200 times.

(a) Work out an estimate for the number of times the dice will land on a four.

........................ Total 2 marks)


31. Amy is going to play one game of snooker and one game of billiards.

The probability that she will win the game of snooker is 4

3

The probability that she will win the game of billiards is 3

1

Complete the probability tree diagram.

(Total 2 marks)

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