Foundation November 2017 Paper 3 Q14
14 A shop records the time taken by its customers to complete a purchase on its website.
The results from one day are summarised in this table.
| Time taken (\(t\) minutes) | Number of customers | ||
|---|---|---|---|
| \(0 < t \leqslant 3\) | 6 | ||
| \(3 < t \leqslant 6\) | 10 | ||
| \(6 < t \leqslant 9\) | 6 | ||
| \(9 < t \leqslant 12\) | 2 | ||
| \(12 < t \leqslant 15\) | 1 |
(a) Calculate an estimate of the mean time taken. [4]
(b) Explain why it is not possible to use the information from this table to calculate the exact value of the mean time taken. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5.34 | 4 | B1 for 1.5, 4.5, 7.5, 10.5, 13.5 M1FT for 1.5 \(\times\) 6 4.5 \(\times\) 10 7.5 \(\times\) 6 10.5 \(\times\) 2 13.5 \(\times\) 1 soi 9, 45, 45, 21, 13.5 or 133.5 M1 for their 133.5 \(\div\) 25 | At least 4 midpoints correct FT midpoints or either end of range values consistently used Allow one numerical error Four correct products or 133.5 imply B1 and M1 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Exact times for each customer are not recorded oe | 1 | Do not accept, “Because the mid-point is used” or comments on the method used. | |