A-LevelMathematicsProbability and statistics9709/53 · May/June 2025 · Q14 Marks

For a set of 40 values of x, it is found that Σ(x-k) = 836.0, Σ(x−k)² = 25410.8, where k is a constant.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[B1] 4960-40k=836 or 4960/40 - k = 836/40 OE. Also accept 124 – k = 20.9 or 40k = 4124 OE.
[B1] k=103.1
[M1] [sd² =] 25410.8/40 - (836/40)²
[A1] [sd² = 198.46, ] sd = 14.1 (14.08758...to at least 3SF. If M not awarded SCB1 for correct answer WWW.)
[M1] [sd² =] 622978.4/40 - 124² (622978.4 comes from expansion of Σ(x – k)² = 25410.8 substituting in relevant values.)
[A1] [sd² = 198.46, ] sd = 14.1 (14.08758...to at least 3SF. If M not awarded SCB1 for correct answer WWW.)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2025 Paper 5 Variant 3, question 1.

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