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The Oakwood Academy
Page 1
Histograms (Interpreting)
The Oakwood Academy
Page 2
Q1.Jon uses this data about the heights of plants (h) to draw the histogram below.
Height, h (cm)
0 < h ≤ 10 10 < h ≤ 20 20 < h ≤ 30 30 < h ≤ 45 45 < h ≤ 50
Frequency 7 8 3 6 5
Heights of plants
Height, h (cm)
Write down three different types of mistake that he has made.
Mistake 1 .................................................................................................................
Mistake 2 .................................................................................................................
Mistake 3 ................................................................................................................. (Total 3 marks)
The Oakwood Academy
Page 3
Q2.The table and histogram give some information about the heights of 120 children.
Height, h (cm)
Frequency
40 < h ≤ 60 30
60 < h ≤ 70 20
70 < h ≤ 75
75 < h ≤ 95 50
95 < h ≤ 105
Total = 120
(a) Complete the table and the histogram. (3)
(b) Calculate an estimate of the upper quartile of the heights of the 120 children.
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Answer ................................................................ cm (2)
(Total 5 marks)
The Oakwood Academy
Page 4
Q3.A company has 800 workers. The table and histogram show the distribution of weekly wages.
Weekly wages, w (£) Frequency
0 < w ≤ 100
100 < w ≤ 200 150
200 < w ≤ 250 140
250 < w ≤ 300 120
300 < w ≤ 500
500 < w ≤ 600 20
Total800
Complete both the table and the histogram. (Total 4 marks)
The Oakwood Academy
Page 5
Q4.The table and histogram show some information about the cholesterol level in the blood of 100 hospital patients.
Cholesterol level, c Frequency
0 < c ≤ 2 8
2 < c ≤ 3 13
3 < c ≤ 4
4 < c ≤ 5 19
5 < c ≤ 7
7 < c ≤ 10 15
(a) Use the table to complete the histogram. (2)
(b) Use the histogram to complete the table. (2)
(Total 4 marks)
The Oakwood Academy
Page 6
Q5.The histogram shows information about the distances 600 people travel to work.
(a) How many people travel more than 20 miles to work?
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Answer ...................................................................... (2)
(b) 224 of these people travel further to work than I do.
Estimate the distance I travel to work.
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Answer ............................................................ miles (4)
(Total 6 marks)
The Oakwood Academy
Page 7
Q6.The histogram represents the birth masses of 500 mice.
Birth mass (grams)
Work out the number of mice with birth masses below 10 grams.
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Answer ...................................................................... (Total 4 marks)
The Oakwood Academy
Page 8
Q7. The histogram shows the ages, in years, of members of a chess club.
There are 22 members with ages in the range 40 ≤ age < 65
Work out the number of members with ages in the range 25 ≤ age < 40
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Answer ............................................ (Total 4 marks)
The Oakwood Academy
Page 9
Q8.(a) The histogram shows information about 200 internet users.
How many of these internet users are aged under 20?
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Answer ...................................................................... (3)
The Oakwood Academy
Page 10
Q9. The histogram shows the time it takes 270 students to travel to school.
Travel to school
Kirsty says 30% of the students take more than 25 minutes to travel to school.
Is she correct? Use the histogram to decide. You must show your working.
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Answer ...................................................................... (Total 5 marks)
The Oakwood Academy
Page 11
Q10.Kate and David are a team in a contest. They will each have one chance to estimate a minute.
(a) Kate has 200 practice attempts.
Based on her practice attempts, show that the probability that she can estimate a minute to within one second is 0.67
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........................................................................................................................ (2)
The Oakwood Academy
Page 12
Q11.Here are the histograms for four different sets of data. Each set of data has the same number of values.
Histogram 1
Histogram 2
Histogram 3
Histogram 4
The Oakwood Academy
Page 13
Here are the box plots for the same four sets of data.
Box plot A
Box plot B
Box plot C
Box plot D
Complete the table to match each box plot to a histogram.
Histogram Box plot
1
2
3
4
(Total 3 marks)
The Oakwood Academy
Page 14
Q12.Hamza made this hypothesis,
“60% of hospital patients wait between 20 and 40 minutes”.
He collects data about the waiting times of 360 patients.
Hospital waiting times
Does the data support his hypothesis? You must show your working.
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The Oakwood Academy
Page 15
Q13.The histogram shows information about the ages of 100 employees.
Work out an estimate of the median age of the employees.
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Answer ......................................................................years (Total 4 marks)
The Oakwood Academy
Page 16
Q14. 70 people gave information about the number of hours they worked in one week. The table and histogram show some of that information.
Number of hours, n Frequency
0 < n ≤ 10 21
10 < n ≤ 20 x
20 < n ≤ 40 y
40 < n ≤ 50 17
x : y = 3 : 5
Complete the histogram. Remember to label the scale on the frequency density axis.
(Total 6 marks)
The Oakwood Academy
Page 17
Q15. The histogram represents the weights, in kilograms, of the people on a fitness course.
(a) Work out the total number of people on the fitness course.
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Answer ...................................................................... (3)
(b) Six more people join the course. They each weigh between 120 kilograms and 130 kilograms.
Complete the histogram. (1)
(Total 4 marks)
The Oakwood Academy
Page 18
Q16.The histogram represents the heights of 90 firefighters.
(a) Which of the four bars represents the greatest number of firefighters? You must show your working.
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Answer ............................. cm ≤ height (3)
(b) Calculate an estimate of the mean height. You must show your working.
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Answer ................................................................... cm (4)
The Oakwood Academy
Page 19
(c) The tallest firefighter was 195.6 cm The shortest firefighter was 170.4 cm
Both heights are given to 1 decimal place.
Work out the maximum possible difference in their heights.
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Answer ................................................................... cm (2)
(Total 9 marks)