A-LevelMathematicsProbability and statistics9709/61 · May/June 2018 · Q13 Marks

In a statistics lesson 12 people were asked to think of a number, x, between 1 and 20 inclusive. From the results Tom found that Σx = 186 and that the standard deviation of x is 4.5. Assuming that Tom's calculations are correct, find the values of Σ(x – 10) and Σ(x – 10)2.

In a statistics lesson 12 people were asked to think of a number, x, between 1 and 20 inclusive. From the results Tom found that Σx = 186 and that the standard deviation of x is 4.5. Assuming that Tom's calculations are correct, find the values of Σ(x – 10) and Σ(x – 10)2.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[B1] Σ(x – 10) = 186 - 12 × 10 = 66
[M1] Consistent substituting in the correct coded variance formula OR Valid method for Σx² then expanding Σ(x – 10)², 3 terms with at least 2 correct
[B1] Σ(x – 10)² = 606

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source: A-Level Mathematics, May/June 2018 Paper 6 Variant 1, question 1.

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