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O-LevelMathematicsStatistics4024/22 · Oct/Nov 2022 · Q211 Marks

Marco grows two types of tomato plants, type A and type B. He counts the number of tomatoes growing on each tomato plant. The results for type A plants are shown in the table. Number of tomatoes on plant: 17, 18, 19, 20, 21, 22. Frequency: 5, 2, 7, 3, 2, 1.

  1. (a)(i)Calculate the mean number of tomatoes per plant.[2]
  2. (a)(ii)Calculate the range.[1]
  3. (a)(iii)The mean number of tomatoes per plant for type B plants is 17.1 and the range is 8. Make two comments comparing the number of tomatoes growing on type A and type B plants. 1 2[2]
  4. (b)(i)Marco also grows strawberries. He records the masses, m grams, of 120 of his strawberries. The frequency table shows the results. Mass (m grams): 5 < m ≤ 10, 10 < m ≤ 15, 15 < m ≤ 20, 20 < m ≤ 25, 25 < m ≤ 30. Frequency: 15, 38, 45, 17, 5. Draw a cumulative frequency diagram to represent these results. [Figure with cumulative frequency grid][3]
  5. (b)(ii)Marco uses strawberries with a mass greater than 21 grams to make jam. Use your diagram to find an estimate for the percentage of strawberries he uses to make jam.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [2] M1 for (17×5+18×2 + 19×7 + 20×3+ 21×2 + 22×1) ÷ (5+2 + 7 + 3 + 2 + 1)
  2. [1]
  3. [2] Strict FT their mean and range B1FT for each
  4. [3] B2 for 4 or 5 points plotted correctly or B1 for 4 or 5 correct cumulative frequencies soi
  5. [3] M1 for correct reading of their increasing curve at m = 21 M1 for (120-y)/120 [×100]

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About this question

Topic
Statistics, O-Level Mathematics (syllabus 4024). Structured question, 11 marks.
Source
O-Level Mathematics, Oct/Nov 2022 Paper 2 Variant 2, question 2.

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