Lemmara logoLemmaraWorked solution

4MA1/1H Jun 2021, Question 18: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Using a frequency table and histogram of distances travelled to work by store employees, complete the table and histogram, then estimate the probability a randomly chosen person travelled over 25 km.

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

Part (a) · 2 marks

Use the histogram bar heights and the given frequencies to work out the missing frequencies for the table.

  1. 1Bar 0−10: frequency density 40 ÷ 10 = 4, drawn 20 small squares tall, so 1 small square = 0.2
  2. 210−15: 35 squares = 7, so frequency 7 × 5 = 35
  3. 315−20: 39 squares = 7.8, so frequency 7.8 × 5 = 39
  4. 420−30: 28 squares = 5.6, so frequency 5.6 × 10 = 56
  5. 5The missing frequencies are 35, 39, 56

Answer35, 39, 56

Part (b) · 1 mark

Draw the missing bar on the histogram for the 30 to 60 km class.

  1. 1Frequency density = 30 ÷ (60 − 30) = 1
  2. 21 small square = 0.2, so the bar is 5 small squares tall
  3. 3A bar from 30 to 60 at a frequency density of 1

AnswerA bar from 30 to 60 at a frequency density of 1

Part (c) · 2 marks

Estimate the probability that a randomly chosen person travelled more than 25 km.

  1. 1Total frequency = 40 + 35 + 39 + 56 + 30 = 200
  2. 2Distance > 25 km is part of 20 ≤ d < 30 and all of 30 ≤ d < 60
  3. 3In 20 ≤ d < 30: half the distance range is above 25, so estimate half the frequency: 0.5 × 56 = 28
  4. 4Add frequency for 30 ≤ d < 60: 28 + 30 = 58
  5. 5Probability = 58 / 200 = 29 / 100

Answer29/100

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

Practise more histograms (unequal class intervals) questions

Real 4MA1 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: 4MA1 1H June 2021 · 4MA1/1H · 4ma1 jun21 1h · question 18.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.