A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2017 · Q46 Marks

The ages of a group of 12 people at an Art class have mean 48.7 years and standard deviation 7.65 years. The ages of a group of 7 people at another Art class have mean 38.1 years and standard deviation 4.2 years.

(i)Find the mean age of all 19 people.[2]
(ii)The individual ages in years of people in the first Art class are denoted by x and those in the second Art class by y. By first finding Σx² and Σy², find the standard deviation of the ages of all 19 people.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] (i) (48.7×12+38.1×7) / 19 (Accept unsimplified (may be separate calculations))
[1] (i) = 44.8
[1] (ii) Substitution in one correct variance formula
[1] (ii) One Σx² or Σy² correct (can be rounded to 4sf))
[1] (ii) Using their Σx² and Σy² and their 4(i) in the variance formula
[1] (ii) Combined σ = 8.37 or 8.36

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2017 Paper 6 Variant 1, question 4.

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