Difficultyeasier → harder · picks a 20-mark mix in order of difficulty. Print, top right.
Assessment · Histograms
20 marks
Answer all questions. Show all your working; you get marks for method. Work on your own.Name: __________ Class: ______ Date: ______
The table shows the height of some plants. Work out the frequency density of the class $15 < h \le 25$.
Height, h (cm)
Frequency
0 < h ≤ 5
10
5 < h ≤ 15
10
15 < h ≤ 25
20
25 < h ≤ 30
10
30 < h ≤ 40
15
Answer: (2 marks)
In a histogram, the class $10 < h \le 20$ has a frequency of 15. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the time of some runners. Work out the frequency density of the class $20 < t \le 30$.
Time, t (min)
Frequency
0 < t ≤ 20
60
20 < t ≤ 30
10
30 < t ≤ 40
5
40 < t ≤ 50
5
Answer: (2 marks)
In a histogram, the class $30 < s \le 34$ has a frequency of 4. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the speed of some cars. Work out the frequency density of the class $30 < s \le 40$.
Speed, s (mph)
Frequency
0 < s ≤ 10
5
10 < s ≤ 30
60
30 < s ≤ 40
15
40 < s ≤ 60
30
Answer: (2 marks)
In a histogram, the class $10 < s \le 20$ has a frequency of 25. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the height of some plants. Work out the frequency density of the class $30 < h \le 40$.
Height, h (cm)
Frequency
0 < h ≤ 20
50
20 < h ≤ 30
15
30 < h ≤ 40
25
40 < h ≤ 50
5
Answer: (2 marks)
In a histogram, the class $30 < w \le 45$ has a frequency of 15. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the speed of some cars. Work out the frequency density of the class $40 < s \le 50$.
Speed, s (mph)
Frequency
0 < s ≤ 10
30
10 < s ≤ 20
25
20 < s ≤ 40
60
40 < s ≤ 50
15
Answer: (2 marks)
In a histogram, the class $10 < w \le 18$ has a frequency of 32. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the time of some runners. Work out the frequency density of the class $20 < t \le 40$.
Time, t (min)
Frequency
0 < t ≤ 10
30
10 < t ≤ 20
25
20 < t ≤ 40
20
40 < t ≤ 50
30
Answer: (2 marks)
In a histogram, the class $50 < t \le 65$ has a frequency of 45. Work out the frequency density for this class.
Answer: (2 marks)
The table shows the weight of some parcels. Work out the frequency density of the class $5 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 5
10
5 < w ≤ 15
10
15 < w ≤ 25
20
25 < w ≤ 30
5
30 < w ≤ 40
5
Answer: (2 marks)
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $10 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 10
15
10 < w ≤ 15
5
15 < w ≤ 20
5
20 < w ≤ 30
30
30 < w ≤ 50
50
Answer: (2 marks)
The histogram shows the time of some runners. Estimate how many had a time between 40 and 50 min.
Answer: (2 marks)
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $0 < t \le 5$.
Time, t (min)
Frequency
0 < t ≤ 5
?
5 < t ≤ 15
20
15 < t ≤ 25
15
25 < t ≤ 30
20
30 < t ≤ 40
15
Answer: (2 marks)
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $40 < t \le 50$.
Time, t (min)
Frequency
0 < t ≤ 10
30
10 < t ≤ 20
20
20 < t ≤ 40
40
40 < t ≤ 50
30
Answer: (2 marks)
The histogram shows the height of some plants. Estimate how many had a height between 15 and 20 cm.
Answer: (2 marks)
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $25 < s \le 30$.
Speed, s (mph)
Frequency
0 < s ≤ 5
20
5 < s ≤ 15
5
15 < s ≤ 25
25
25 < s ≤ 30
?
30 < s ≤ 40
30
Answer: (2 marks)
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $10 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 10
5
10 < w ≤ 15
10
15 < w ≤ 20
5
20 < w ≤ 30
30
30 < w ≤ 50
30
Answer: (2 marks)
The histogram shows the speed of some cars. Estimate how many had a speed between 0 and 5 mph.
Answer: (2 marks)
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $20 < s \le 40$.
Speed, s (mph)
Frequency
0 < s ≤ 10
15
10 < s ≤ 20
30
20 < s ≤ 40
?
40 < s ≤ 50
25
Answer: (2 marks)
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $30 < h \le 40$.
Height, h (cm)
Frequency
0 < h ≤ 5
10
5 < h ≤ 15
25
15 < h ≤ 25
10
25 < h ≤ 30
15
30 < h ≤ 40
10
Answer: (2 marks)
The histogram shows the weight of some parcels. Estimate how many had a weight between 20 and 30 kg.
Answer: (2 marks)
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $20 < h \le 30$.
Height, h (cm)
Frequency
0 < h ≤ 10
15
10 < h ≤ 15
20
15 < h ≤ 20
10
20 < h ≤ 30
?
30 < h ≤ 50
20
Answer: (2 marks)
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $20 < h \le 30$.
Height, h (cm)
Frequency
0 < h ≤ 20
40
20 < h ≤ 30
5
30 < h ≤ 40
15
40 < h ≤ 50
15
Answer: (2 marks)
The histogram shows the speed of some cars. Estimate how many had a speed between 5 and 40 mph.
Answer: (3 marks)
On this histogram each small square represents 5 runners. Estimate how many runners had a time between 10 and 20 min.
Answer: (3 marks)
A histogram is drawn for the weight of some parcels. The class $10 < w \le 30$ contains 60 parcels. Using the heights of the bars, estimate how many are in the class $40 < w \le 60$.
Answer: (3 marks)
The histogram shows the speed of some cars. Estimate the percentage of cars with a speed between 20 and 40 mph.
Answer: (3 marks)
The histogram shows the weight of 70 parcels. One of the parcels is chosen at random. Estimate the probability that its weight is between 40 and 50 kg. Give your answer as a fraction.
Answer: (3 marks)
The histogram shows the speed of some cars. Estimate the total number of cars.
Answer: (3 marks)
The histogram shows the time of some runners. Estimate how many had a time between 5 and 60 min.
Answer: (3 marks)
On a histogram, the bar for $10 < h \le 30$ is taller than the bar for $30 < h \le 40$. The first class has frequency density 3 and the second has frequency density 1. Work out the total number of plants in these two classes.
Answer: (3 marks)
The histogram shows the weight of 110 parcels. The parcels are placed in order of weight. Estimate the weight of the 20th one.
Answer: (3 marks)
Mark scheme · Histograms
Total: 20 marks
Award the marks shown for each correct step, then add up the total out of 20. A method mark counts even if the final answer is wrong.
The table shows the height of some plants. Work out the frequency density of the class $15 < h \le 25$.
Height, h (cm)
Frequency
0 < h ≤ 5
10
5 < h ≤ 15
10
15 < h ≤ 25
20
25 < h ≤ 30
10
30 < h ≤ 40
15
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{20}{10}$.
$= 2$.
Answer: $2$
Marks
✔1 markfrequency ÷ class width = $\dfrac{20}{10}$
✔1 mark2
In a histogram, the class $10 < h \le 20$ has a frequency of 15. Work out the frequency density for this class.[2 marks]
Method
Class width $= 20 - 10 = 10$.
Frequency density $= 15 \div 10 = 1.5$.
Answer: $1.5$
Marks
✔1 markclass width = 10
✔1 mark1.5
The table shows the time of some runners. Work out the frequency density of the class $20 < t \le 30$.
Time, t (min)
Frequency
0 < t ≤ 20
60
20 < t ≤ 30
10
30 < t ≤ 40
5
40 < t ≤ 50
5
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{10}{10}$.
$= 1$.
Answer: $1$
Marks
✔1 markfrequency ÷ class width = $\dfrac{10}{10}$
✔1 mark1
In a histogram, the class $30 < s \le 34$ has a frequency of 4. Work out the frequency density for this class.[2 marks]
Method
Class width $= 34 - 30 = 4$.
Frequency density $= 4 \div 4 = 1$.
Answer: $1$
Marks
✔1 markclass width = 4
✔1 mark1
The table shows the speed of some cars. Work out the frequency density of the class $30 < s \le 40$.
Speed, s (mph)
Frequency
0 < s ≤ 10
5
10 < s ≤ 30
60
30 < s ≤ 40
15
40 < s ≤ 60
30
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{15}{10}$.
$= 1.5$.
Answer: $1.5$
Marks
✔1 markfrequency ÷ class width = $\dfrac{15}{10}$
✔1 mark1.5
In a histogram, the class $10 < s \le 20$ has a frequency of 25. Work out the frequency density for this class.[2 marks]
Method
Class width $= 20 - 10 = 10$.
Frequency density $= 25 \div 10 = 2.5$.
Answer: $2.5$
Marks
✔1 markclass width = 10
✔1 mark2.5
The table shows the height of some plants. Work out the frequency density of the class $30 < h \le 40$.
Height, h (cm)
Frequency
0 < h ≤ 20
50
20 < h ≤ 30
15
30 < h ≤ 40
25
40 < h ≤ 50
5
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{25}{10}$.
$= 2.5$.
Answer: $2.5$
Marks
✔1 markfrequency ÷ class width = $\dfrac{25}{10}$
✔1 mark2.5
In a histogram, the class $30 < w \le 45$ has a frequency of 15. Work out the frequency density for this class.[2 marks]
Method
Class width $= 45 - 30 = 15$.
Frequency density $= 15 \div 15 = 1$.
Answer: $1$
Marks
✔1 markclass width = 15
✔1 mark1
The table shows the speed of some cars. Work out the frequency density of the class $40 < s \le 50$.
Speed, s (mph)
Frequency
0 < s ≤ 10
30
10 < s ≤ 20
25
20 < s ≤ 40
60
40 < s ≤ 50
15
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{15}{10}$.
$= 1.5$.
Answer: $1.5$
Marks
✔1 markfrequency ÷ class width = $\dfrac{15}{10}$
✔1 mark1.5
In a histogram, the class $10 < w \le 18$ has a frequency of 32. Work out the frequency density for this class.[2 marks]
Method
Class width $= 18 - 10 = 8$.
Frequency density $= 32 \div 8 = 4$.
Answer: $4$
Marks
✔1 markclass width = 8
✔1 mark4
The table shows the time of some runners. Work out the frequency density of the class $20 < t \le 40$.
Time, t (min)
Frequency
0 < t ≤ 10
30
10 < t ≤ 20
25
20 < t ≤ 40
20
40 < t ≤ 50
30
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{20}{20}$.
$= 1$.
Answer: $1$
Marks
✔1 markfrequency ÷ class width = $\dfrac{20}{20}$
✔1 mark1
In a histogram, the class $50 < t \le 65$ has a frequency of 45. Work out the frequency density for this class.[2 marks]
Method
Class width $= 65 - 50 = 15$.
Frequency density $= 45 \div 15 = 3$.
Answer: $3$
Marks
✔1 markclass width = 15
✔1 mark3
The table shows the weight of some parcels. Work out the frequency density of the class $5 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 5
10
5 < w ≤ 15
10
15 < w ≤ 25
20
25 < w ≤ 30
5
30 < w ≤ 40
5
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{10}{10}$.
$= 1$.
Answer: $1$
Marks
✔1 markfrequency ÷ class width = $\dfrac{10}{10}$
✔1 mark1
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $10 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 10
15
10 < w ≤ 15
5
15 < w ≤ 20
5
20 < w ≤ 30
30
30 < w ≤ 50
50
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{5}{5}$.
The bar height is $1$.
Answer: $1$
Marks
✔1 markfrequency ÷ class width
✔1 mark1
The histogram shows the time of some runners. Estimate how many had a time between 40 and 50 min.[2 marks]
Method
Read the frequency density of that bar: 1.5. Class width $= 10$.
Frequency $= 1.5 \times 10 = 15$.
Answer: $15$
Marks
✔1 markfrequency density × class width
✔1 mark15
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $0 < t \le 5$.
Time, t (min)
Frequency
0 < t ≤ 5
?
5 < t ≤ 15
20
15 < t ≤ 25
15
25 < t ≤ 30
20
30 < t ≤ 40
15
[2 marks]
Method
From the histogram, frequency density of that bar $= 3$, class width $= 5$.
Frequency $= 3 \times 5 = 15$.
Answer: $15$
Marks
✔1 markfd × width
✔1 mark15
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $40 < t \le 50$.
Time, t (min)
Frequency
0 < t ≤ 10
30
10 < t ≤ 20
20
20 < t ≤ 40
40
40 < t ≤ 50
30
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{30}{10}$.
The bar height is $3$.
Answer: $3$
Marks
✔1 markfrequency ÷ class width
✔1 mark3
The histogram shows the height of some plants. Estimate how many had a height between 15 and 20 cm.[2 marks]
Method
Read the frequency density of that bar: 3. Class width $= 5$.
Frequency $= 3 \times 5 = 15$.
Answer: $15$
Marks
✔1 markfrequency density × class width
✔1 mark15
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $25 < s \le 30$.
Speed, s (mph)
Frequency
0 < s ≤ 5
20
5 < s ≤ 15
5
15 < s ≤ 25
25
25 < s ≤ 30
?
30 < s ≤ 40
30
[2 marks]
Method
From the histogram, frequency density of that bar $= 2$, class width $= 5$.
Frequency $= 2 \times 5 = 10$.
Answer: $10$
Marks
✔1 markfd × width
✔1 mark10
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $10 < w \le 15$.
Weight, w (kg)
Frequency
0 < w ≤ 10
5
10 < w ≤ 15
10
15 < w ≤ 20
5
20 < w ≤ 30
30
30 < w ≤ 50
30
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{10}{5}$.
The bar height is $2$.
Answer: $2$
Marks
✔1 markfrequency ÷ class width
✔1 mark2
The histogram shows the speed of some cars. Estimate how many had a speed between 0 and 5 mph.[2 marks]
Method
Read the frequency density of that bar: 4. Class width $= 5$.
Frequency $= 4 \times 5 = 20$.
Answer: $20$
Marks
✔1 markfrequency density × class width
✔1 mark20
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $20 < s \le 40$.
Speed, s (mph)
Frequency
0 < s ≤ 10
15
10 < s ≤ 20
30
20 < s ≤ 40
?
40 < s ≤ 50
25
[2 marks]
Method
From the histogram, frequency density of that bar $= 2$, class width $= 20$.
Frequency $= 2 \times 20 = 40$.
Answer: $40$
Marks
✔1 markfd × width
✔1 mark40
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $30 < h \le 40$.
Height, h (cm)
Frequency
0 < h ≤ 5
10
5 < h ≤ 15
25
15 < h ≤ 25
10
25 < h ≤ 30
15
30 < h ≤ 40
10
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{10}{10}$.
The bar height is $1$.
Answer: $1$
Marks
✔1 markfrequency ÷ class width
✔1 mark1
The histogram shows the weight of some parcels. Estimate how many had a weight between 20 and 30 kg.[2 marks]
Method
Read the frequency density of that bar: 0.5. Class width $= 10$.
Frequency $= 0.5 \times 10 = 5$.
Answer: $5$
Marks
✔1 markfrequency density × class width
✔1 mark5
The histogram and table show the same data. Use the histogram to find the missing frequency for the class $20 < h \le 30$.
Height, h (cm)
Frequency
0 < h ≤ 10
15
10 < h ≤ 15
20
15 < h ≤ 20
10
20 < h ≤ 30
?
30 < h ≤ 50
20
[2 marks]
Method
From the histogram, frequency density of that bar $= 2$, class width $= 10$.
Frequency $= 2 \times 10 = 20$.
Answer: $20$
Marks
✔1 markfd × width
✔1 mark20
A histogram is to be drawn for this data. Work out the height (frequency density) of the bar for the class $20 < h \le 30$.
Height, h (cm)
Frequency
0 < h ≤ 20
40
20 < h ≤ 30
5
30 < h ≤ 40
15
40 < h ≤ 50
15
[2 marks]
Method
Frequency density $= \dfrac{\text{frequency}}{\text{class width}} = \dfrac{5}{10}$.
The bar height is $0.5$.
Answer: $0.5$
Marks
✔1 markfrequency ÷ class width
✔1 mark0.5
The histogram shows the speed of some cars. Estimate how many had a speed between 5 and 40 mph.[3 marks]
Method
For each bar in the range, frequency = frequency density × width.
Frequencies: 30 + 5 + 15 + 30 = 80.
Answer: $80$
Marks
✔1 markfrequency density × width for each bar
✔1 markAdd the bars in the range
✔1 mark80
On this histogram each small square represents 5 runners. Estimate how many runners had a time between 10 and 20 min.[3 marks]
Method
That bar covers 8 small squares.
Frequency $= 8 \times 5 = 40$.
Answer: $40$
Marks
✔1 markcount squares in the bar = 8
✔1 markmultiply by 5 per square
✔1 mark40
A histogram is drawn for the weight of some parcels. The class $10 < w \le 30$ contains 60 parcels. Using the heights of the bars, estimate how many are in the class $40 < w \le 60$.[3 marks]
Method
The known bar has frequency density $= 60 \div 20 = 3$ (60 over width 20).
Reading the wanted bar at frequency density $1$: frequency $= 1 \times 20 = 20$.
Answer: $20$
Marks
✔1 markfrequency density of known bar = 3
✔1 markapply scale to wanted bar
✔1 mark20
The histogram shows the speed of some cars. Estimate the percentage of cars with a speed between 20 and 40 mph.[3 marks]
Method
Frequency in the range $= 30 = 30$.
Total frequency (all bars) $= 75$, so percentage $= \dfrac{30}{75} \times 100 = 40\%$.
Answer: $40$
Marks
✔1 markrange frequency = 30
✔1 marktotal frequency = 75
✔1 mark40%
The histogram shows the weight of 70 parcels. One of the parcels is chosen at random. Estimate the probability that its weight is between 40 and 50 kg. Give your answer as a fraction.[3 marks]
Method
Frequency of that class $= 2.5 \times 10 = 25$.
Probability $= \dfrac{25}{70} = \dfrac{5}{14}$.
Answer: $\dfrac{5}{14}$
Marks
✔1 markfrequency of class = 25
✔1 marktotal = 70
✔1 mark$\dfrac{5}{14}$
The histogram shows the speed of some cars. Estimate the total number of cars.[3 marks]
Method
Frequency of each bar = frequency density × width: 40, 5, 20, 20.
Total $= 40 + 5 + 20 + 20 = 85$.
Answer: $85$
Marks
✔1 markfd × width for each bar
✔1 markadd all bars
✔1 mark85
The histogram shows the time of some runners. Estimate how many had a time between 5 and 60 min.[3 marks]
Method
Part of the $0 < t \le 10$ bar: width $= 10 - 5 = 5$, so frequency $= 3 \times 5 = 15$.
Whole bars after it total 80. Estimate $= 15 + 80 = 95$.
Answer: $95$
Marks
✔1 markpart-bar frequency = fd × part-width = 15
✔1 markremaining whole bars = 80
✔1 mark95
On a histogram, the bar for $10 < h \le 30$ is taller than the bar for $30 < h \le 40$. The first class has frequency density 3 and the second has frequency density 1. Work out the total number of plants in these two classes.[3 marks]
Method
First class: frequency $= 3 \times 20 = 60$.
Second class: frequency $= 1 \times 10 = 10$. Total $= 60 + 10 = 70$.
Answer: $70$
Marks
✔1 markfirst frequency = 60
✔1 marksecond frequency = 10
✔1 mark70
The histogram shows the weight of 110 parcels. The parcels are placed in order of weight. Estimate the weight of the 20th one.[3 marks]
Method
The first 0 parcels are below 0 kg. We need 20 more into the next class.
That class has frequency density 2, so 20 parcels occupy a width of 20 ÷ 2 = 10. Estimate $= 0 + 10 = 10$ kg.
mathedup.co.uk · sheet 8TRL