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A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2022 · Q14 Marks

The lengths, in millimetres, of a random sample of 12 rods made by a certain machine are as follows. 200 201 198 202 200 199 199 201 197 202 200 199

  1. (a)Find unbiased estimates of the population mean and variance.[3]
  2. (b)Give a statistical reason why these estimates may not be reliable.[1]

Mark scheme

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

  1. [B1] Est (u) = 1199/6 or 199.833 or 200 or 2398/12 [mm]
  2. [M1] Use of their values in correct formula (may be implied)
  3. [A1] = 2.33 (3 sf) [mm²] Accept 7/3
  4. [B1] Small sample Accept not ‘not representative' unless qualified.

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About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Feb/Mar 2022 Paper 6 Variant 2, question 1.

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