HISTOGRAMS
1.
[28]
Table shows the distribution of ages of passengers travelling on a plane from Leeds to Barcelona.
Age (x years)
Frequency
0 < x  20
28
20 < x  35
36
35 < x  45
20
45 < x  65
30
On the grid below, draw a histogram to show this distribution.
75
65
55
45
35
25
15
5
0
10
20
30
40
50
60
70
Age (x years)
(Total 3 marks)
St Trinian’s RC College
1
2.
Steve Oh asked some year 10 students how long they spent doing homework each night.
The histogram was drawn from this information.
Frequency
density
2
1
0
0
10
20
30
40
50
60
Time (t minutes)
70
Use the histogram to complete the table.
Time (t minutes)
Frequency
10  t < 15
10
15  t < 30
36
7.6
22
16
30  t < 40
40  t < 50
50  t < 70
(Total 2 marks)
St Trinian’s RC College
2
3.
4
Frequency
density
in potatoes
per gram 3
2
1
0
10
20
30
40
50
60
Weight in grams
70
80
90
100
The histogram gives information about the weights of some potatoes.
The shaded bar represents 20 potatoes.
(a)
Work out how many of the potatoes weigh 30 grams or less.
..........................
(1)
(b)
Work out how many of the potatoes weigh more than 45 grams.
..........................
(2)
(Total 3 marks)
St Trinian’s RC College
3
4.
Sindre asks some students how long they took to finish their science homework.
The table and histogram show some of this information.
Time (minutes)
Frequency
5 < x  10
15
10 < x  15
20
15 < x  25
60
25 < x  35
50
35 < x  50
15
8
Frequency
Density
7
6
5
4
3
2
1
0
10
20
30
40
50
Time (minutes)
(a)
Use the information in the histogram to complete the table.
(2)
(b)
Use the information in the table to complete the histogram.
(2)
(Total 4 marks)
St Trinian’s RC College
4
5.
The table gives information about the number of hours worked by some factory workers.
Number of hours (n) worked
Frequency
0<n≤5
15
5 < n ≤ 15
42
15 < n ≤ 35
40
35 < n ≤ 50
6
Use the table to draw a histogram.
Frequency
density
5
4
3
2
1
0
10
20
30
40
50
Number of hours (n) worked
(Total 3 marks)
St Trinian’s RC College
5
6.
The table and histogram show information about the length of time it took 165 monkeys to
connect to the internet.
Time (t seconds)
Frequency
0 < t ≤ 10
20
10 < t ≤ 15
15 < t ≤ 17.5
30
17.5 < t ≤ 20
40
20 < t ≤ 25
25 < z ≤ 40
None of the monkeys took more than 40 seconds to connect to the internet.
(a)
Use the table to complete the histogram.
(2)
(b)
Use the histogram to complete the table.
Frequency
density
O
5
10
15
20
25
30
35
40
Time (seconds)
(2)
(Total 4 marks)
St Trinian’s RC College
6
7.
The table and histogram show some information about the area of some magical Persian carpets...
Carpet area
(A m2)
Frequency
10 < A  12
12 < A  15
15
15 < A  20
12
20 < A  25
10
Frequency
density
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Carpet area ( A m 2)
(a)
Use the histogram to complete the table.
(1)
(b)
Use the table to complete the histogram.
(2)
(Total 3 marks)
St Trinian’s RC College
7
8.
A group of students takes an English test.
The results are shown in the histogram.
5
4
Frequency
density
3
2
1
0
10
20
30
40
50
60
70
80
90
100
Mark (x)
100 students score marks in the range 50 < x ≤ 75.
(i)
How many students score marks in the range 0 < x ≤ 50?
[1]
(ii)
How many students score marks in the range 75 < x ≤ 100?
[1]
(iii)
Calculate an estimate of the mean mark of this group of students.
[4]
(Total 6 marks)
St Trinian’s RC College
8