A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2022 · Q13 Marks

The heights, in metres, of a random sample of 10 mature trees of a certain variety are given below. 5.9 6.5 6.7 5.9 6.9 6.0 6.4 6.2 5.8 5.8 Find unbiased estimates of the population mean and variance of the heights of all mature trees of this variety.

Find unbiased estimates of the population mean and variance of the heights of all mature trees of this variety.[3]

Mark scheme

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

[B1] 62.1 / 10 = 6.21 OE
[M1] [Σχ² = 387.05] 10/9 their '387.05'/10 -(their '6.21')² or 1/9 (their '387.05' - (their '6.21')²/10)
[A1] = 0.157 (3 sf) or 1409/9000

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, Oct/Nov 2022 Paper 6 Variant 1, question 1.

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