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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 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
.
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●
Level 4
4 marks
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→
Mark as done
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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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)
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●
Level 4
4 marks
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Interpreting histograms
12 questions
Lesson
Not started
Mark as done
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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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.
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●
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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→
Mark as done
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
Start
→
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)
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Level 4
4 marks
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