Histograms
Probability and statistics
- Higher
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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A histogram bar runs from $0$ to $10$ and has frequency density $0.8$. Find the frequency.
2 marks
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A bar runs from $10$ to $30$ and has frequency density $0.6$. Find the frequency.
2 marks
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The histogram shows four classes. Read the frequency densities and find the four frequencies. The class widths are $5$, $10$, $20$ and $5$.
Histogram. The number above each bar is its frequency density. 3 marks
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For that histogram, which class has the greatest frequency density, and which has the greatest frequency?
3 marks
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Using the same histogram, estimate how many values are above $15$.
4 marks
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A class from $20$ to $40$ has frequency $16$. The other bars represent $24$ people. Find the frequency density of the missing bar and the total frequency.
4 marks
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A histogram represents $50$ people. The class $0$ to $10$ has frequency density $0.6$, $10$ to $20$ has frequency density $1.4$, and $40$ to $50$ has frequency density $0.8$. The missing class is $20$ to $40$. Find its frequency and frequency density.
5 marks
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For the histogram in question $7$, how many people scored less than $20$? Estimate how many scored between $30$ and $50$, and explain why the second answer is an estimate.
6 marks
Mark scheme
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Answer. $8$
- Frequency $= \text{frequency density} \times \text{class width}$
- $0.8 \times 10 = 8$
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Answer. $12$
- The class width is $20$.
- $0.6 \times 20 = 12$
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Answer. Densities $2, 1.2, 0.4, 1$. Frequencies $10, 12, 8, 5$.
- The labels on the bars are the frequency densities.
- Frequencies $= 2 \times 5$, $1.2 \times 10$, $0.4 \times 20$ and $1 \times 5$.
- $10, 12, 8, 5$
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Answer. Greatest density: $0$ to $5$. Greatest frequency: $5$ to $15$.
- The tallest bar is $0$ to $5$, with density $2$.
- The greatest frequency is $12$, in the class $5$ to $15$.
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Answer. $13$
- The classes $15$ to $35$ and $35$ to $40$ are completely above $15$.
- $8 + 5 = 13$
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Answer. Frequency density $0.8$, total frequency $40$
- Class width $= 20$, so the density is $\dfrac{16}{20} = 0.8$.
- Total frequency $= 24 + 16 = 40$.
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Answer. Frequency $22$, frequency density $1.1$
- Known frequencies $= 6 + 14 + 8 = 28$.
- The missing frequency is $50 - 28 = 22$.
- Density $= \dfrac{22}{20} = 1.1$.
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Answer. $20$ people scored less than $20$. About $19$ scored between $30$ and $50$. The $30$ boundary splits a class, so the estimate assumes the values are spread evenly.
- Less than $20$: $6 + 14 = 20$.
- From $30$ to $40$ is half of the $20$ to $40$ class, so about $11$ people.
- Add the $8$ people from $40$ to $50$, giving $19$.
- The split of the wide class is an estimate, not an exact count.