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22 questions at your level
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Level 2
Level 3
Level 4
Level 5
Histograms & frequency density
13 questions
Lesson
Not started
Mark as done
The table shows information about the masses,
m
m
m
kilograms, of 70 suitcases checked in at an airport desk.
Mass,
m
m
m
(kg)
Frequency
0
<
m
≤
20
0 < m \le 20
0
<
m
≤
20
36
20
<
m
≤
30
20 < m \le 30
20
<
m
≤
30
22
30
<
m
≤
60
30 < m \le 60
30
<
m
≤
60
12
(a)
Work out the frequency density of each class.
(b)
Ravi says, "The class
0
<
m
≤
20
0 < m \le 20
0
<
m
≤
20
must have the tallest bar on the histogram, because it has the largest frequency."
Is Ravi correct? Explain your answer.
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Level 2
3 marks
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The histogram shows information about the weights,
w
w
w
grams, of the letters posted at a post box one morning.
20
40
60
80
100
1
2
3
4
Weight, w (grams)
Frequency density
(a)
Work out the number of letters that weighed more than
60
60
60
g.
(b)
Work out the total number of letters posted.
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Level 3
5 marks
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The table shows information about the distances,
d
d
d
metres, thrown by each of 100 competitors at a school sports day.
Distance,
d
d
d
(m)
Frequency
0
≤
d
<
10
0 \le d < 10
0
≤
d
<
10
20
10
≤
d
<
25
10 \le d < 25
10
≤
d
<
25
45
25
≤
d
<
30
25 \le d < 30
25
≤
d
<
30
20
30
≤
d
<
50
30 \le d < 50
30
≤
d
<
50
15
(a)
Draw a histogram for this information.
(b)
Explain why the vertical axis of your histogram must be labelled "Frequency density" and not "Frequency".
●●●
●●
Level 3
4 marks
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The table shows the ages of
44
44
44
people at a club.
Age,
a
a
a
(years)
Frequency
0
<
a
≤
10
0 < a \le 10
0
<
a
≤
10
8
10
<
a
≤
15
10 < a \le 15
10
<
a
≤
15
12
15
<
a
≤
25
15 < a \le 25
15
<
a
≤
25
15
25
<
a
≤
40
25 < a \le 40
25
<
a
≤
40
9
(a)
Work out the frequency density for the
15
<
a
≤
25
15 < a \le 25
15
<
a
≤
25
class. (1 mark)
(b)
Estimate the number of people older than
20
20
20
. (2 marks)
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Level 3
3 marks
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The histogram shows information about the heights,
h
h
h
cm, of some plants.
10
20
30
40
50
60
0.5
1
1.5
2
2.5
3
Height, h (cm)
Frequency density
(a)
Work out the number of plants with a height between
10
10
10
cm and
20
20
20
cm. (2 marks)
(b)
There are
6
6
6
plants with a height greater than
30
30
30
cm.
Work out an estimate for the number of plants with a height greater than
25
25
25
cm. (2 marks)
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Level 3
4 marks
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The table shows the lengths,
l
l
l
cm, of
62
62
62
fish.
Length,
l
l
l
(cm)
Frequency
0
<
l
≤
5
0 < l \le 5
0
<
l
≤
5
10
5
<
l
≤
15
5 < l \le 15
5
<
l
≤
15
24
15
<
l
≤
20
15 < l \le 20
15
<
l
≤
20
12
20
<
l
≤
40
20 < l \le 40
20
<
l
≤
40
16
(a)
Work out the frequency density of the
5
<
l
≤
15
5 < l \le 15
5
<
l
≤
15
class. [1]
(b)
Estimate the number of fish with lengths between
10
10
10
cm and
20
20
20
cm. [2]
●●●
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Level 3
3 marks
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The times,
t
t
t
minutes, that 100 customers spent in a shop were recorded and shown on a histogram. The histogram below is incomplete: the bar for the class
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
has not been drawn.
10
20
30
40
50
60
0.5
1
1.5
2
2.5
3
Time, t (minutes)
Frequency density
(a)
Work out the number of customers who spent between
20
20
20
and
30
30
30
minutes in the shop.
(b)
Work out the height of the bar that should be drawn for the class
20
<
t
≤
30
20 < t \le 30
20
<
t
≤
30
.
●●●●
●
Level 4
4 marks
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The lengths of 84 nails were each measured to the nearest millimetre. The results are shown in the table.
Length (mm)
Frequency
20–24
16
25–29
24
30–39
30
40–59
14
(a)
Explain why the class 25–29 has a class width of 5 and not 4.
(b)
Work out the frequency density of each of the four classes.
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●
Level 4
4 marks
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→
Mark as done
Chloe timed each of 65 people answering a question. Her results are in the table.
Time,
s
s
s
(seconds)
Frequency
0
<
s
≤
10
0 < s \le 10
0
<
s
≤
10
12
10
<
s
≤
15
10 < s \le 15
10
<
s
≤
15
18
15
<
s
≤
20
15 < s \le 20
15
<
s
≤
20
15
20
<
s
≤
40
20 < s \le 40
20
<
s
≤
40
20
She then drew the chart below, using the frequency of each class as the height of its bar.
10
20
30
40
5
10
15
20
Time, s (seconds)
Frequency (Chloe's heights)
Chloe says, "My chart shows that the
20
<
s
≤
40
20 < s \le 40
20
<
s
≤
40
group is the busiest."
(a)
Explain why Chloe's chart is misleading.
(b)
Work out the correct height of each bar for a histogram of this data.
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●
Level 4
4 marks
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The histogram gives information about the times, in minutes, that some people spent in a library one day.
The histogram is incomplete.
0
10
20
30
40
50
60
70
80
Time (minutes)
Frequency density
32
32
32
people spent between
25
25
25
and
35
35
35
minutes in the library.
36
36
36
people spent between
45
45
45
and
75
75
75
minutes in the library.
(a)
Use this information to complete the histogram.
(2 marks)
Nobody spent more than
75
75
75
minutes in the library.
(b)
Work out the total number of people.
(2 marks)
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●
Level 4
4 marks
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The histogram gives information about the heights, in cm, of some seedlings.
2
4
6
8
10
12
14
16
18
20
22
24
1
2
3
4
5
6
7
8
9
10
11
Height (cm)
Frequency density
One of these seedlings is picked at random.
Work out an estimate for the probability that the height of this seedling is between
5
5
5
cm and
13
13
13
cm.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
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A histogram is drawn to represent a set of values of
t
t
t
. It has exactly three bars.
Class
Frequency density
0
<
t
≤
8
0 < t \le 8
0
<
t
≤
8
2.5
8
<
t
≤
20
8 < t \le 20
8
<
t
≤
20
4.5
20
<
t
≤
k
20 < t \le k
20
<
t
≤
k
1.2
The bar for the class
20
<
t
≤
k
20 < t \le k
20
<
t
≤
k
represents 30 values.
(a)
Work out the value of
k
k
k
.
(b)
Work out the total number of values represented by the histogram.
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Level 5
6 marks
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A histogram showing the masses,
m
m
m
grams, of some parcels is drawn on squared paper. There is
no scale
on the frequency density axis.
The bar for the class
0
<
m
≤
20
0 < m \le 20
0
<
m
≤
20
is
4
4
4
cm wide and
3
3
3
cm high, and it represents 24 parcels.
(a)
The bar for the class
20
<
m
≤
30
20 < m \le 30
20
<
m
≤
30
is
2
2
2
cm wide and
4.5
4.5
4.5
cm high. Work out the number of parcels it represents.
(b)
The class
30
<
m
≤
45
30 < m \le 45
30
<
m
≤
45
contains 45 parcels. Its bar is
3
3
3
cm wide. Work out the height of that bar.
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Level 5
6 marks
Start
→
Interpreting histograms
12 questions
Lesson
Not started
Mark as done
10
20
30
40
50
60
0.5
1
1.5
2
2.5
3
Time (minutes)
Frequency density
The histogram gives information about the times, in minutes, that some students spent on homework one evening.
(a)
Work out the number of students who spent between
20
20
20
and
40
40
40
minutes on homework.
(b)
Work out the total number of students.
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●●●
Level 2
4 marks
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→
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10
20
30
40
50
60
70
80
0.5
1
1.5
2
2.5
Age (years)
Frequency density
The histogram gives information about the ages of the members of a swimming club.
(a)
Estimate the number of members aged between
20
20
20
and
30
30
30
.
(b)
Explain why your answer to part (a) is only an estimate.
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●●
Level 3
3 marks
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10
20
30
40
50
60
0.5
1
1.5
2
2.5
3
Distance (km)
Frequency density
The histogram gives information about the distances, in kilometres, that the employees of a company travel to work.
Estimate the number of employees who travel between
15
15
15
km and
30
30
30
km to work.
●●●
●●
Level 3
3 marks
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Mark as done
The histogram shows information about the heights,
h
h
h
cm, of some plants.
10
20
30
40
50
60
0.5
1
1.5
2
2.5
3
Height, h (cm)
Frequency density
(a)
Work out the number of plants with a height between
10
10
10
cm and
20
20
20
cm. (2 marks)
(b)
There are
6
6
6
plants with a height greater than
30
30
30
cm.
Work out an estimate for the number of plants with a height greater than
25
25
25
cm. (2 marks)
●●●
●●
Level 3
4 marks
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→
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10
20
30
40
50
60
70
0.5
1
1.5
2
2.5
3
Time (seconds)
Frequency density
The histogram gives information about the times, in seconds, taken by a group of students to solve a puzzle.
Work out an estimate for the mean time taken.
●●●●
●
Level 4
4 marks
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Mark as done
10
20
30
40
50
60
70
0.5
1
1.5
2
2.5
3
3.5
Height (cm)
Frequency density
The histogram gives information about the heights, in centimetres, of the plants in a nursery.
(a)
Work out the total number of plants.
(b)
Write down the class interval that contains the median height.
●●●●
●
Level 4
4 marks
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20
40
60
80
100
120
140
0.5
1
1.5
2
2.5
3
Lifetime (hours)
Frequency density
The histogram gives information about the lifetimes, in hours, of
160
160
160
batteries.
(a)
Estimate the number of batteries with a lifetime between
50
50
50
hours and
80
80
80
hours.
(b)
One of the
160
160
160
batteries is chosen at random. Estimate the probability that its lifetime is at least
100
100
100
hours.
●●●●
●
Level 4
5 marks
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The histogram shows the ages of the people at a swimming pool one afternoon.
20
40
60
80
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Age (years)
Frequency density
(a)
Work out the total number of people at the pool. [2]
(b)
Estimate the number of people aged between
25
25
25
and
45
45
45
. [2]
(c)
Which class interval contains the median age? [1]
●●●●
●
Level 4
5 marks
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The histogram gives information about the times, in minutes, that some people spent in a library one day.
The histogram is incomplete.
0
10
20
30
40
50
60
70
80
Time (minutes)
Frequency density
32
32
32
people spent between
25
25
25
and
35
35
35
minutes in the library.
36
36
36
people spent between
45
45
45
and
75
75
75
minutes in the library.
(a)
Use this information to complete the histogram.
(2 marks)
Nobody spent more than
75
75
75
minutes in the library.
(b)
Work out the total number of people.
(2 marks)
●●●●
●
Level 4
4 marks
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Mark as done
The histogram gives information about the heights, in cm, of some seedlings.
2
4
6
8
10
12
14
16
18
20
22
24
1
2
3
4
5
6
7
8
9
10
11
Height (cm)
Frequency density
One of these seedlings is picked at random.
Work out an estimate for the probability that the height of this seedling is between
5
5
5
cm and
13
13
13
cm.
(4 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
A bank recorded the waiting times, in minutes, of its customers at two branches on the same morning.
Branch A
(
80
80
80
customers)
10
20
30
40
50
60
0.5
1
1.5
2
2.5
Waiting time (minutes)
Frequency density
Branch B
(
100
100
100
customers)
10
20
30
40
50
60
0.5
1
1.5
2
2.5
Waiting time (minutes)
Frequency density
(a)
Estimate the number of customers at branch A who waited less than
20
20
20
minutes.
(b)
Estimate the number of customers at branch B who waited less than
20
20
20
minutes.
(c)
Use the histograms to compare the waiting times at the two branches.
●●●●●
Level 5
6 marks
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10
20
30
40
50
60
70
80
1
2
3
4
Amount spent (£)
Frequency density
The histogram gives information about the amounts of money spent by the shoppers in a shop one morning.
(a)
Work out an estimate for the median amount spent.
(b)
Rani says, "More than a quarter of these shoppers spent at least £
40
40
40
."
Is Rani correct? You must show your working.
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Level 5
6 marks
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