Topic 2

Data

1. Jerry recorded the colour of each of the cars he saw one morning.

The bar chart shows this information.

(a) Write down the number of red cars.

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

(1)

(b) Which was the most popular colour of car?

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

(1)

(Total 2 marks)

2. José is in hospital.

Here is his temperature chart during one day.

(a) At what time was José’s temperature 39.0°C?

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

(1)

(b) What can you say about José’s temperature from 6 am to 6 pm?

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

(1)

(Total 2 marks)

12

10

8

6

4

2

0

white black red yellow

Colour

Numberof cars

6 7 8 9 10 11 12 1 2 3 4 5 6

36.0

36.5

37.0

37.5

38.0

38.5

39.0

39.5

40.0

40.5

Time pmam

12. Here is a bar chart showing the number of hours of TV that Helen and Robin

watched last week.

(a) Write down the number of hours of TV that Helen watched on Monday.

………………………hours

(1)

(b) On which day did Helen and Robin watch the same number of hours of TV?

………………………

(1)

(c) (i) Work out the total number of hours of TV that Robin watched on Friday and

Saturday.

………………………hours

(ii) Who watched the greater number of hours of TV on Friday and Saturday? Show

your working.

(3)

(Total 5 marks)

9

8

7

6

5

4

3

2

1

0

Number of hours Helen

Robin

Hours of TV watched last week

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Day

1. Chloe made a list of her homework marks.

4 5 5 5 4 3 2 1 4 5

(a) Write down the mode of her homework marks.

…………………….

(1)

(b) Work out her mean homework mark.

…………………….

(2)

(Total 3 marks)

2. Peter rolled a 6-sided dice ten times.

Here are his scores.

3 2 4 6 3 3 4 2 5 4

(a) Work out the median of his scores.

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

(2)

(b) Work out the mean of his scores.

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

(2)

(c) Work out the range of his scores.

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

(1)

(Total 5 marks)

7. Mr Smith kept a record of the number of absences for each student in his

class for one term.

Here are his results.

0 0 0 8 4 5 5 3 2 1

(a) Write down the mode.

………………...

(1)

(b) Work out the mean.

………………...

(2)

(Total 3 marks)

8. Here are 10 numbers.

3 2 5 4 2 4 6 2 1 2

(a) Find the mode of these numbers.

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

(1)

(b) Find the median of these numbers.

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

(2)

(c) Find the range of these numbers.

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

(2)

(Total 5 mark)

1. The pictogram shows the numbers of loaves of bread made by Miss Smith,

Mr Jones and

Mrs Gray.

Miss Smith

Mr Jones

Mrs Gray

Ms Shah

Mr Khan

represents 20 loaves of bread

(a) Write down the number of loaves of bread made by Mr Jones.

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

(1)

(b) Write down the number of loaves of bread made by Mrs Gray.

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

(1)

Ms Shah made 60 loaves of bread.

Mr Khan made 90 loaves of bread.

(c) Use this information to complete the pictogram.

(2)

(Total 4 marks)

8. Felicity asked 100 students how they came to school one day.

Each student walked or came by bicycle or came by car.

49 of the 100 students are girls.

10 of the girls came by car.

16 boys walked.

21 of the 41 students who came by bicycle are boys.

Work out the total number of students who walked to school.

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

(4 marks)

1. The table gives information about the numbers of fish in a lake.

Fish Frequency

Perch 10

Bream 23

Carp 39

Draw an accurate pie chart to show this information.

(4 marks)

5. Some children were asked to name their favourite flavour of ice cream.

The pie chart and table show some information about their answers.

Use the pie chart to complete the table.

Flavour Number of children Angle of sector

vanilla 12 90°

mint .................................. 45°

strawberry 14 ..................................

chocolate .................................. 120°

(3 marks)

6. Noreen carries out a survey of some students.

The pie chart shows some information about their favourite holiday.

5 students said that walking is their favourite holiday.

(a) How many students took part in the survey?

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

(2)

Noreen chooses one of these students at random.

(b) Write down the probability that this student’s favourite holiday is cycling. .........................

(1)

(3 marks)

1. The scatter graph shows some information about 8 cars.

For each car it shows the engine size, in litres, and the distance, in kilometres, the car travels on one

litre of petrol.

(a) What type of correlation does the scatter graph show?

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

(1)

A different car of the same type has an engine size of 2.5 litres.

(b) Estimate the distance travelled on one litre of petrol by this car.

.............................................. kilometres

(2)

(3 marks)

______________________________________________________________________________

6. Some students took a mathematics test and a science test.

The scatter graph shows information about the test marks of eight students.

The table shows the test marks of four more students.

Mark in mathematics test 14 25 50 58

Mark in science test 21 23 38 51

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

(2)

(b) Describe the correlation between the marks in the mathematics test and the marks in the science

test.

…………………………………………………..

(1)

Josef was absent for the mathematics test but his mark in the science test was 45

(c) Estimate Josef’s mark in the mathematics test.

…………………………..

(2)

(5 marks)

______________________________________________ ____________________________

60

50

40

30

20

10

00 10 20 30 40 50 60

Mark in mathematics test

Markinsciencetest

2. The table shows some information about the weights, in kg, of 100 boxes.

Weight of box (w kg) Frequency

0 < w 4 10

4 < w 8 17

8 < w 12 28

12 < w 16 25

16 < w 20 20

Draw a frequency polygon to show this information.

(4 marks)

6. The table gives information about the lengths of the branches on a bush.

Length(Lcm) Frequency

0 L <10 20

10 L < 20 12

20 L < 30 10

30 L < 40 8

40 L < 50 6

50 L < 60 0

(a) Draw a frequency polygon to show this information.

(3)

(b) Write down the modal class interval.

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

(1)

One of the branches is chosen at random.

(c) Work out the probability that this branch less than 20 cm long.

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

(2)

(6 marks)

______________________________________________________________________________

1. 3. Here are the ages, in years, of 15 students.

19 18 20 25 37

33 21 17 29 20

42 18 23 37 22

Show this information in an ordered stem and leaf diagram.

(3 marks)

__________________________________________________________________________

2. Jo measured the times in seconds it took 18 students to run 400 m.

Here are the times.

67 78 79 98 96 103

75 85 94 92 61 80

82 86 90 95 90 89

(a) Draw an ordered stem and leaf diagram to show this information.

(3)

(b) Work out the median.

..................................... seconds

(2)

(5 marks)

3. Here are the speeds, in miles per hour, of 16 cars.

31 52 43 49 36 35 33 29

54 43 44 46 42 39 55 48

Draw an ordered stem and leaf diagram for these speeds.

(4 marks)

__________________________________________________________________________

4. Here are some people’s ages in years.

62 27 33 44 47

30 22 63 67 54

69 56 63 50 25

31 63 42 48 51

In the space below, draw an ordered stem and leaf diagram to show these ages.

(4 marks)

7. Jan measures the heights, in millimetres, of 20 plants in her greenhouse.

Here are her results.

178 189 147 147 166

167 153 171 164 158

189 166 165 155 152

147 158 148 151 172

Complete the stem and leaf diagram to show this information.

Stem Leaf

__________________________________________________________________(4 marks)

8. Anil counted the number of letters in each of 30 sentences in a newspaper.

Anil showed his results in a stem and leaf diagram.

0 8 8 9

1 1 2 3 4 4 8 9

2 0 3 5 5 7 7 8

3 2 2 3 3 6 6 8 8

4 1 2 3 3 5

Key 4 1 stands for 41 letters

(a) Write down the number of sentences with 36 letters. ..............................

(1)

(b) Work out the range. ..............................

(1)

(c) Work out the median.

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

(2)

(4 marks)

9. Here are the weights, in kilograms, of 15 parcels.

1.1 1.7 2.0 1.0 1.1 0.5 3.3 2.0

1.5 2.6 3.5 2.1 0.7 1.2 0.6

Draw a stem and leaf diagram to show this information.

(Total 3 marks)

11. Here are the ages, in years, of 15 teachers.

35 52 42 27 36

23 31 41 50 34

44 28 45 45 53

(a) Draw an ordered stem and leaf diagram to show this information.

You must include a key.

(3)

One of these teachers is picked at random.

(b) Work out the probability that this teacher is more than 40 years old.

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

(2)

(Total 5 marks)

Key:

1.

The diagram shows a fair spinner in the shape of a rectangular octagon.

The spinner can land on A or B or C.

Marc spins the spinner.

Write down the probability that the spinner will land on A.

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

(Total 2 marks)

2. Ishah spins a fair 5-sided spinner.

She then throws a fair coin.

(a) List all the possible outcomes she could get.

The first one has been done for you.

(1, head).........................................................................................................

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

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

(2)

Ishah spins the spinner once and throws the coin once.

(b) Work out the probability that she will get a 1 and a head.

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

(1)

(Total 3 marks)

A

A

A

B

B B

B

C

3. There are eight marbles in a bag.

Four marbles are blue (B),

two marbles are red (R)

and two marbles are green (G).

Steve takes a marble at random from the bag.

(a) On the probability scale, mark with the letter B, the probability that

Steve will take a blue marble.

(1)

(b) On the probability scale, mark with the letter G, the probability that

Steve will take a green marble.

(1)

(c) On the probability scale, mark with the letter Y, the probability that

Steve will take a yellow marble.

(1)

(Total 3 marks)

G

R

B

BG

BR

B

2

10 1

2

10 1

2

10 1

1. The probability that a biased dice will land on a five is 0.3

Megan is going to roll the dice 400 times.

Work out an estimate for the number of times the dice will land on a five.

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

_______________________________________________________________________(2 marks)

2. Jack sows 300 wildflower seeds.

The probability of a seed flowering is 0.7

Work out an estimate for the number of these seeds that will flower.

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

________________________________________________________________________(2 marks)

3. Angel Ltd manufacture components for washing machines. The probability that a component

will be made within a tolerance of one tenth of a millimetre is 0.995.

Angel Ltd. manufacture 10 000 components each day.

Work out an estimate for the number of components that will not be within the tolerance of

one tenth of a millimetre each day.

________________________________________________________________________(2 marks)

7. A bag contains only red, green and blue counters.

The table shows the probability that a counter chosen at random from the bag will be red

or will be green.

Colour Red Green Blue

Probability 0.5 0.3

Mary takes a counter at random from the bag.

(a) Work out the probability that Mary takes a blue counter.

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

(2)

The bag contains 50 counters.

(b) Work out how many green counters there are in the bag.

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

(2)

________________________________________________________________________(4 marks)

8. A bag contains counters which are blue or red or green or yellow.

Mark takes a counter at random from the bag.

The table shows the probabilities he takes a blue counter or a red counter or a yellow

counter.

Colour Blue red green yellow

Probability 0.3 0.2 0.1

(a) Work out the probability that Mark takes a green counter.

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

(2)

Mark puts the counter back into the bag.

Laura takes a counter at random from the bag.

She looks at its colour then puts the counter back into the bag.

She does this 50 times.

(b) Work out an estimate for the number of times Laura takes a red counter.

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

(2)

________________________________________________________________________(4 marks)

3. Andy did a survey of the number of cups of coffee some pupils in his school had drunk

yesterday.

The frequency table shows his results.

Number of cups of

coffee Frequency

2 1

3 3

4 5

5 8

6 5

(a) Work out the number of pupils that Andy asked. .....................................

(2)

(b) Work out the mean number of cups of coffee drunk. .....................................

(3)

(5 marks)

4. 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

(a) Write down the modal number of goals scored.

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

(1)

(b) Work out the range of the number of goals scored.

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

(1)

(c) Work out the mean number of goals scored.

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

(3)

(5 marks)

5. Bob asked each of 40 friends how many minutes they took to get to work.

The table shows some information about his results.

Time taken (m minutes) Frequency

0 < m 10 3

10 < m 20 8

20 < m 30 11

30 < m 40 9

40 < m 50 9

a) Work out an estimate for the mean time taken.

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

b) State the modal class interval

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

c) Find the group containing the median

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

(7 marks)

______________________________________________________________________________

9. 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

(a) Work out an estimate for the mean weight of the pebbles.

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

(3)

(b) Write down the modal class interval.

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

(1)

(c) Find the class interval that contains the median.

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

(2)

(d) Why is your answer to part (a) and estimate?

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

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

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

(1)

(7 marks)

2. Sameena recorded the times, in minutes, some girls took to do a jigsaw puzzle.

Sameena used her results to work out the information in this table.

Minutes

Shortest time 18

Lower quartile 25

Median 29

Upper quartile 33

Longest time 44

(a) On the grid, draw a box plot to show the information in the table.

(2)

The box plot below shows information about the times, in minutes, some boys took to do the same

jigsaw puzzle.

(b) Compare the distributions of the girls’ times and the boys’ times.

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

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

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

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

(2)

(4 marks)

______________________________________________________________________________

4. Harry grows tomatoes.

This year he put his tomato plants into two groups, group A and group B.

Harry gave fertiliser to the tomato plants in group A.

He did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group A.

The cumulative frequency graph shows some information about these weights.

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

.............................................. g

(1)

The 60 tomatoes from group A

had a minimum weight of 153 grams

and a maximum weight of 186 grams.

(b) Use this information and the cumulative frequency graph to draw a box plot for the 60 tomatoes

from group A.

(3)

Harry did not give fertiliser to the tomato plants in group B.

Harry weighed 60 tomatoes from group B.

He drew this box plot for his results.

(c) Compare the distribution of the weights of the tomatoes from group A with the distribution of

the weights of the tomatoes from group B.

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

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

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

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

(2)

(6 marks)

______________________________________________________________________________

5. The table shows information about the speeds of 100 lorries.

Speed (s) in km/h Frequency

0 < s 20 2

20 < s 40 9

40 < s 60 23

60 < s 80 31

80 < s 100 27

100 < s 120 8

(a) Complete the cumulative frequency table for this information.

Speed (s) in km/h Cumulative

frequency

0 < s 20 2

0 < s 40

0 < s 60

0 < s 80

0 < s 100

0 < s 120

(1)

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

(2)

(c) Find an estimate for the number of lorries with a speed of more than 90 km/h.

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

(2)

(5 marks)

______________________________________________________________________________

1. Hannah is going to play one badminton match and one tennis match.

The probability that she will win the badminton match is 10

9

The probability that she will win the tennis match is 5

2

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that Hannah will win both matches.

(2)

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

(4 marks)

2. There are only red marbles and green marbles in a bag.

There are 5 red marbles and 3 green marbles.

Dwayne takes at random a marble from the bag.

He does not put the marble back in the bag.

Dwayne takes at random a second marble from the bag.

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that Dwayne takes marbles of different colours.

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

(3)

(5 marks)

5. Carolyn has 20 biscuits in a tin.

She has

12 plain biscuits

5 chocolate biscuits

3 ginger biscuits

Carolyn takes at random two biscuits from the tin.

Work out the probability that the two biscuits were not the same type.

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

(4 marks)

______________________________________________________________________________