The mean of the weekly grocery bills, in pounds, for a household over 6 weeks is \(£58\). The bills for the first five of these weeks are \(£52\), \(£61\), ...
Question 1 Report
The mean of the weekly grocery bills, in pounds, for a household over 6 weeks is \(£58\). The bills for the first five of these weeks are \(£52\), \(£61\), \(£55\), \(£64\) and \(£59\).
- Work out the total of the bills for all 6 weeks. (1)
- Work out the bill for the sixth week. (2)
Answer Details
This question tests using a known mean to recover a total, then subtracting the known values to find a missing one.
(a) Since the mean of the 6 weekly bills is £58, the total of all 6 bills is
\[ 58 \times 6 = £348 \] [1 mark]
(b) Subtracting the five known bills from this total leaves the sixth week's bill:
\[ 348 - (52 + 61 + 55 + 64 + 59) = 348 - 291 = £57 \] [2 marks]
Multiplying the mean by the number of values to recover the total, then subtracting the known values, is the standard technique whenever one value in a mean is missing.
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