Households on a street are surveyed by a local researcher about their weekly grocery spend, rounded to the nearest £10, as part of a study into the cost of ...
Question 1 Report
Households on a street are surveyed by a local researcher about their weekly grocery spend, rounded to the nearest £10, as part of a study into the cost of living. The table shows the amount spent and the number of households reporting it.
| Amount spent (£) | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|
| Number of households | 3 | 7 | 9 | 5 | 2 |
- Write down the modal amount spent. (1)
- Work out the range of the amounts spent. (1)
- Work out the mean amount spent per household. (2)
Answer Details
The mode is read straight from the highest frequency, the range compares the extreme amounts spent, and the mean uses every household's spending weighted by how many households reported it.
- The highest frequency is \(9\), at \(\pounds30\), so the modal amount spent is \(\pounds30\). [1 mark]
- Range = \(\pounds50-\pounds10=\pounds40\). [1 mark]
- Total spend: \(10\times3+20\times7+30\times9+40\times5+50\times2=30+140+270+200+100=740\). Total households: \(3+7+9+5+2=26\). Mean = \(740\div26=\pounds28.46\) (2 d.p.). [2 marks]
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