Lemmara logoLemmaraWorked solution

4024/12 Oct/Nov 2022, Question 20: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Table gives reading times for 100 children in four intervals with some frequencies and frequency densities; find the missing lower bound x, then draw a histogram of the data.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Using the frequency 32 and frequency density 1.6 for the first interval, find the value of x.

  1. 1Class width = frequency ÷ frequency density = 32 ÷ 1.6 = 20
  2. 2x = 30 − 20 = 10

Answer10

Part (b) · 3 marks

On the grid with time axis 0 to 60 and frequency density axis 0 to 4, draw a histogram for all 100 children.

  1. 1Frequency densities: 40 < t ≤ 45: 15 ÷ 5 = 3; 45 < t ≤ 60: 30 ÷ 15 = 2
  2. 2Draw bars: 10 to 30 height 1.6, 30 to 40 height 2.3
  3. 340 to 45 height 3, 45 to 60 height 2
  4. 4No gaps between the bars

AnswerCorrect histogram

Stuck on a step? Read the free lesson: Histograms (Unequal Class Intervals)

Practise more histograms (unequal class intervals) questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on histograms (unequal class intervals)

Also searched as: 4024/12/O/N/22 · 4024_w22_qp_12 · 4024 w22 12 · question 20.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.