3 A group of 60 students were each asked their favourite fruit. The results are shown in the table. Fruit Frequency Apple 20 Banana 25 Orange 15 Complete the pie chart to show the results. Apple [2]

3 Sector 150° labelled banana Sector 90° labelled orange 2 B1 for 90° or 150° seen or sector with correct angle drawn To earn marks, you need to draw a sector for banana with a 150° angle and label it, and a sector for orange with a 90° angle and label it. You can also earn a mark for just showing either 90° or 150° calculated, or for drawing one of the sectors with the correct angle.

11 (a) In a survey, 3 out of every 100 women were taller than 1.9 m. One of these 100 women is picked at random. Calculate the probability that she is not taller than 1.9 m. … [1] (b) A new housing estate is being planned. There are three possible plans: A, B and C. A survey was carried out to see which plan people preferred. The relative frequency table shows the results. Plan A B C Relative frequency 0.3 0.5 0.2 52 people preferred plan C. (i) Find how many people preferred plan A. … [2] (ii) Calculate the total number of people surveyed. … [1]

11(a) 0.97 or 97 100 1 11(b)(i) 78 2 M1 for 52 ÷ [0.]2 oe or 52 × 1.5 oe 11(b)(ii) 260 1 For part (a), you must state the probability as 0.97 or 97/100. For part (b)(i), you must correctly find the number of people who preferred plan A; one mark is awarded for correctly dividing 52 by 0.2 or multiplying 52 by 1.5. For part (b)(ii), you must correctly state the total number of people surveyed.

16 A 4‑sided spinner numbered 1 to 4 is spun many times. The table shows the results of the spins. Number Frequency 1 6 2 5 3 13 4 p (a) The mean of the results is 3. Calculate the value of p. p = … [3] (b) Find the relative frequency of the spinner landing on 2. … [1]

16(a) 17 3 M2 for 3 1 6 2 5 3 13 4 6 5 13 × + × + × = + + + + p p oe or M1 for either 1× 6 + 2 × 5 + 3 × 13 + 4p or for 3 (6 5 13 ) × + + + p 16(b) 5 41 oe 1 FT 5 24 + their (a) (a) To earn marks, you must set up an equation where the sum of (number × frequency) equals the mean multiplied by the total frequency, then solve for p. (b) To earn marks, you must state the frequency of landing on 2 divided by the total number of spins, which includes the calculated value of p.

21 The cumulative frequency diagram shows the masses, m grams, of 120 eggs. m 30 0 20 40 60 80 100 120 40 50 Mass (grams) Cumulative frequency 60 70 (a) Use the diagram to estimate (i) the median, … g [1] (ii) the interquartile range. … g [2] (b) Eggs are described as ‘large’ if their mass is 63 g or more. How many of these eggs are large? … [2]

21(a)(i) 58 1 21(a)(ii) 11 2 B1 for 62 or 51 written 21(b) 21 to 24 2 B1 for 96 to 99 written

24 A group of office workers are each asked to record the distance, d kilometres, they travel to work. The results for some of their journeys are shown in the histogram. 0 Frequency density 0 1 2 3 4 5 6 15 30 Distance (km) 10 25 40 5 20 35 d There were 20 workers in the d 0 5 1 G group. (a) There were 12 workers in the d 20 40 1 G group. Complete the histogram. [1] (b) Calculate the percentage of workers who travelled more than 20 km to work. … % [3]

24(a) Correct bar height 0.6 1 24(b) 15 3 M2 for [ ] 12 100 20 6 5 1.8 10 12 × + × + × + or M1 for 6 × 5 and 1.8 × 10 soi as frequencies (a) To earn this mark, a student must draw the bar for the 0 20 (which is 12 + 10 + 1.8 = 23.8) and then express this as a percentage of the total number of workers (20 + 12 + 10 + 1.8 = 43.8), or show the calculation (12 + 10 + 1.8) / (20 + 12 + 10 + 1.8) * 100. Partial credit is given for correctly calculating the frequencies for the given bars (e.g., 6 * 5 = 30 and 1.8 * 10 = 18) or for correctly identifying the number of workers in the d > 20 group as 12 + 10 + 1.8 = 23.8.

Cambridge O Level Mathematics (Syllabus D) · 4024

O-Level Mathematics (Syllabus D) (4024) Statistics past paper questions

Revise O-Level Mathematics (Syllabus D) (4024) — Statistics with real Cambridge past-paper questions grouped by topic, each shown with its marking scheme. Working one topic at a time targets exactly the skill each question tests.

74 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.