Averages (including IQR): WJEC GCSE Intermediate June 2024 Unit 2 Q18

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Intermediate June 2024 Unit 2 Q18

18. \(a\) and \(b\) are two numbers, where \(b \gt a\).

The mean of the two numbers is equal to the range of the two numbers.

Show that \(3a = b\). [3]

Mark scheme

Scheme	Marks	Comments
\(\dfrac{a + b}{2} = b - a\)	B1	Award B0 for \(a + b \div 2 = b - a\) unless brackets are implied in later correct workings.
\(a + b = 2(b - a)\)	B1	May be implied by correct further work (e.g. \(a + b = 2b - 2a\)).
\(a + b = 2b - 2a\) or \(a + 2a = 2b - b\) \((= 3a = b)\)	B1	Award final B1 only from convincing work. If no marks, award SC1 for one of the following: \(a + b \div 2 = b - a\) \(\dfrac{a + b}{2} = a - b\) sight of \(\dfrac{a + b}{2}\) AND \(b - a\) showing the result is true (mean = range) for a pair of values \(a\) and \(b\) (where \(3a = b\)) e.g. stating that \(a\) = 3 and \(b\) = 9 and that (9 + 3) ÷ 2 = 6 and 9 – 3 = 6.