4MA0 Foundation June 2017 Paper 2R Q22
22 The frequency table shows information about the distances 60 office workers travel to work each day.
| Distance travelled (\(d\) km) | Frequency |
|---|---|
| \(0 \lt d \leqslant 10\) | 5 |
| \(10 \lt d \leqslant 20\) | 12 |
| \(20 \lt d \leqslant 30\) | 17 |
| \(30 \lt d \leqslant 40\) | 20 |
| \(40 \lt d \leqslant 50\) | 6 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean distance travelled to work by these office workers.
Give your answer correct to 1 decimal place. (4)
Give your answer correct to 1 decimal place. (4)
| Scheme | Marks |
|---|---|
| \(30 \lt d \leqslant 40\) | B1 |
| (1) |
Notes
B1: Accept 30 – 40
| Scheme | Marks |
|---|---|
| 5×5 + 15×12 + 25×17 + 35×20 + 45×6 or 25 + 180 + 425 + 700 + 270 or 1600 | M2 |
| \(\dfrac{25 + 180 + 425 + 700 + 270}{5 + 12 + 17 + 20 + 6}\) or \(\left(= \dfrac{1600}{60}\right)\) | M1 |
| 26.7 | 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 (ft their products)
NB: accept their 60 if addition of frequencies is shown
A1: Accept 26.6 – 26.7 inclusive
Accept 27 if M3 awarded
Do not accept fractions or mixed numbers, eg \(\dfrac{80}{3}\) or \(26\dfrac{2}{3}\)