4024/22 Oct/Nov 2021, Question 2: Histograms (Unequal Class Intervals)
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks
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The question, in short
Use a pie chart of ages at a science fair and a grouped frequency table of 250 competition scores to find a modal class, a count, a histogram and a distinction percentage.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (ai) · 1 mark
State the age group with the highest frequency from the pie chart.
- 1Largest sector is 144°, so modal class = 16 to 20
Answer16 to 20
Part (aii) · 2 marks
Given 90 people aged over 30, use the 54° and 144° sectors to calculate how many are 16 to 20.
- 154° represents 90 people
- 216 to 20: 90/54 × 144 = 240
Answer240
Part (bi) · 3 marks
Complete the histogram by drawing bars for the score groups using frequency density, with 70 < s ≤ 80 already drawn.
- 1Frequency density = frequency ÷ class width
- 20−40: 36 ÷ 40 = 0.9; 40−60: 48 ÷ 20 = 2.4; 60−70: 64 ÷ 10 = 6.4; 80−100: 42 ÷ 20 = 2.1
- 3Draw bars on these bases with these heights (70−80 already drawn at 6)
AnswerCorrect histogram
Part (bii) · 2 marks
Estimate the percentage of the 250 students scoring 75 or more, using the 70 < s ≤ 80 and 80 < s ≤ 100 groups.
- 175 to 80: half of 60 = 30; 80 to 100: 42
- 2Distinction ≈ 30 + 42 = 72
- 372/250 × 100 = 28.8%
Answer28.8
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