4MA0 Foundation January 2017 Paper 1 Q23
23 The table gives information about the distances, in kilometres, Darren travelled to deliver 100 parcels.
| Distance travelled (\(d\) km) | Frequency |
|---|---|
| \(0 \lt d \leqslant 5\) | 28 |
| \(5 \lt d \leqslant 10\) | 32 |
| \(10 \lt d \leqslant 15\) | 20 |
| \(15 \lt d \leqslant 20\) | 14 |
| \(20 \lt d \leqslant 25\) | 6 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean distance Darren travelled to deliver these parcels. (4)
| Scheme | Marks |
|---|---|
| \(5 \lt d \leqslant 10\) | B1 |
| (1) |
Notes
B1: accept 5 – 10
| Scheme | Marks |
|---|---|
| 2.5 × 28 + 7.5 × 32 + 12.5 × 20 + 17.5 × 14 + 22.5 × 6 or 70 + 240 + 250 + 245 + 135 or 940 | M2 |
| (2.5 × 28 + 7.5 × 32 + 12.5 × 20 + 17.5 × 14 + 22.5 × 6) ÷ 100 or (70 + 240 + 250 + 245 + 135) ÷ 100 or “940” ÷ 100 | M1 |
| 9.4 | A1 |
| (4) | |
| (5 marks) |
Notes
M2: \(f \times d\) for at least 4 products with correct mid-interval values and intention to add
If not M2 then award M1 for
\(d\) used consistently for at least 4 products within interval (including end points) and intention to add
or
for at least 4 correct products with correct mid-interval values with no intention to add
M1: dep on M1
NB: accept their 100 if addition shown
A1: SC: B2 for answer of 9.44
(B1 for 944 in working)