5
5
400
300
Cumulative
200
frequency Field A
100
0 10 20 30 40 50
Height (cm)
The diagram above is the cumulative frequency curve for the heights of 400 plants which
were grown in Field A.
Use the graph to find
(a) the number of plants that grew to a height of more than 30 cm,
(b) the interquartile range.
Answer (a) ........................................... [1]
(b) ........................................... [1]
(c) Another 400 plants were grown in Field B.
The cumulative frequency distribution of the heights of these plants is shown in the
table.
Height (h cm) h 10 h 15 h 20 h 25 h 30 h 35 h 40 h 50
Cumulative
frequency 35 75 130 200 280 330 370 400
On the same axes as for Field A, draw the cumulative frequency curve for the plants
grown in Field B. [2]
(d) By comparing the two curves, state, with a reason, which Field produced the taller
plants.
Answer (d) Field .......... produced the taller plants because ...................................................
, 9
10 (a) Fifty students were asked how many books they each took to school on Monday.
The results are summarised in the table below.
Number of books 0 1 2 3 4 5 6 7
Frequency 10 11 8 3 6 7 4 1
(i) Write down the median.
(ii) Calculate the mean number of books.
(iii) What is the probability that two students, chosen at random, both took 5 books to
school?
Give your answer as a fraction in its simplest form.
Answer (a)(i) ........................................[1]
(ii) .........................................[3]
(iii) ........................................[2]
(b) The fifty students were also asked how long they each took to travel to school.
The results are summarised in the table below.
Time of travel (t minutes) 4⭐t<6 6⭐t<8 8 ⭐ t < 10 10 ⭐ t < 12
Frequency 21 11 13 5
Draw a frequency polygon on the grid below to illustrate this data.
Answer (b)
25
20
15
Frequency
10
5
0
Time (t minutes)
[2]
5
400
300
Cumulative
200
frequency Field A
100
0 10 20 30 40 50
Height (cm)
The diagram above is the cumulative frequency curve for the heights of 400 plants which
were grown in Field A.
Use the graph to find
(a) the number of plants that grew to a height of more than 30 cm,
(b) the interquartile range.
Answer (a) ........................................... [1]
(b) ........................................... [1]
(c) Another 400 plants were grown in Field B.
The cumulative frequency distribution of the heights of these plants is shown in the
table.
Height (h cm) h 10 h 15 h 20 h 25 h 30 h 35 h 40 h 50
Cumulative
frequency 35 75 130 200 280 330 370 400
On the same axes as for Field A, draw the cumulative frequency curve for the plants
grown in Field B. [2]
(d) By comparing the two curves, state, with a reason, which Field produced the taller
plants.
Answer (d) Field .......... produced the taller plants because ...................................................
, 9
10 (a) Fifty students were asked how many books they each took to school on Monday.
The results are summarised in the table below.
Number of books 0 1 2 3 4 5 6 7
Frequency 10 11 8 3 6 7 4 1
(i) Write down the median.
(ii) Calculate the mean number of books.
(iii) What is the probability that two students, chosen at random, both took 5 books to
school?
Give your answer as a fraction in its simplest form.
Answer (a)(i) ........................................[1]
(ii) .........................................[3]
(iii) ........................................[2]
(b) The fifty students were also asked how long they each took to travel to school.
The results are summarised in the table below.
Time of travel (t minutes) 4⭐t<6 6⭐t<8 8 ⭐ t < 10 10 ⭐ t < 12
Frequency 21 11 13 5
Draw a frequency polygon on the grid below to illustrate this data.
Answer (b)
25
20
15
Frequency
10
5
0
Time (t minutes)
[2]
