Foundation November 2024 Paper 1 Q18
18 The table shows some information about the hourly rates of pay of 60 workers.
| Hourly rate of pay (\(p\) dollars) | Frequency |
|---|---|
| \(10 \lt p \leqslant 15\) | 18 |
| \(15 \lt p \leqslant 20\) | 16 |
| \(20 \lt p \leqslant 25\) | 14 |
| \(25 \lt p \leqslant 30\) | 8 |
| \(30 \lt p \leqslant 35\) | 4 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean hourly rate of pay of the 60 workers. (4)
| Scheme | Marks |
|---|---|
| \(10 \lt p \leqslant 15\) | B1 |
| (1) |
Notes
B1: allow \(10 \leqslant p \leqslant 15\) or \(10 \lt p \lt 15\) or
\(10 \leqslant p \lt 15\) or 10 – 15
| Scheme | Marks |
|---|---|
| 12.5 × 18 + 17.5 × 16 + 22.5 × 14 + 27.5 × 8 + 32.5 × 4 (= 1170) or 225 + 280 + 315 + 220 + 130 (= 1170) [lower bound products are: 180, 240, 280, 200, 120] [upper bound products are: 270, 320, 350, 240, 140] Sum of lower bound products = 1020 Sum of upper bound products = 1320 Sum of products using 11, 16, 21, 26 and 31 = 1080 Sum of products using 12, 17, 22, 27 and 32 = 1140 Sum of products using 13, 18, 23, 28 and 33 = 1200 Sum of products using 14, 19, 24, 29 and 34 = 1260 | M2 |
| “1170” ÷ 60 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 19.5 | A1 |
| (4) | |
| (5 marks) |
Notes
M2: for at least 4 correct products added (need not be evaluated) or
If not M2 then award:
M1 for consistent use of value within interval (including end points) for at least 4 products which must be added
or
correct midpoints used for at least 4 products and not added
M1: dep on at least M1
Allow division by their \(\Sigma f\) provided addition or total under column seen
A1: oe