Higher January 2023 Paper 1R Q1
1 The table shows information about the frame size, in cm, of 60 bicycles sold in a shop.
| Frame size (\(S\) cm) | Frequency |
|---|---|
| \(30 \lt S \leqslant 36\) | 4 |
| \(36 \lt S \leqslant 42\) | 14 |
| \(42 \lt S \leqslant 48\) | 18 |
| \(48 \lt S \leqslant 54\) | 19 |
| \(54 \lt S \leqslant 60\) | 5 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean frame size. (4)
| Scheme | Marks |
|---|---|
| \(48 \lt S \leqslant 54\) | B1 |
| (1) |
Notes
B1: Allow 48 – 54 oe
| Scheme | Marks |
|---|---|
| (33 × 4) + (39 × 14) + (45 × 18) + (51 × 19) + (57 × 5) or 132 + 546 + 810 + 969 + 285 (= 2742) [lower bound products are: 120, 504, 756, 912, 270] [upper bound products are: 144, 588, 864, 1026, 300] | M2 |
| \(\dfrac{\text{``}{2742}\text{''}}{60}\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 45.7 | A1oe |
| (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 M1
Allow division by their \(\Sigma f\) provided addition or total under column seen
A1oe: \(45\frac{7}{10}\) or \(\dfrac{457}{10}\) (accept 46 from correct working)