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A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q37 Marks

The mean and standard deviation of 20 values of x are 60 and 4 respectively.

  1. (i)Find the values of Σx and Σx².[3]
  2. (ii)Another 10 values of x are such that their sum is 550 and the sum of their squares is 40 500. Find the mean and standard deviation of all these 30 values of x.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1] Σx = 60×20 = 1200
  2. [M1] Correct variance formula used, condone = 4
  3. [A1] Σx² = 72320
  4. [M1] Summing both values of Σx and Σx²
  5. [B1FT] Mean = their 1750/30 = 58.3
  6. [M1] substitute their Σx and Σx² into correct variance formula
  7. [A1] s.d. = 18.9

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 6 Variant 1, question 3.

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