Foundation November 2023 Paper 2 Q21
21. Regan caught 70 fish on a fishing trip.
He measured the length of each of the fish in centimetres.
The table shows his results.
| Length, \(l\) (centimetres) | Number of fish |
|---|---|
| \(60 \leqslant l \lt 65\) | 19 |
| \(65 \leqslant l \lt 70\) | 17 |
| \(70 \leqslant l \lt 75\) | 23 |
| \(75 \leqslant l \lt 80\) | 10 |
| \(80 \leqslant l \lt 85\) | 1 |
(a) Calculate an estimate for the mean length of these fish. [4]
(b)
Regan thinks that the median length of fish is in the group \(70 \leqslant l \lt 75\).
Is Regan correct?
Yes ☐ No ☐
Give the reason for your answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| Mid-points 62.5 67.5 72.5 77.5 82.5 | B1 | May be implied from correct totals, see below |
| 62.5 × 19 + 67.5 × 17 + 72.5 × 23 + 77.5 × 10 + 82.5 × 1 | M1 | FT ‘their mid-points’ provided at least 4 of these are at the bounds or within the groups 1187.5 + 1147.5 + 1667.5 + 775 + 82.5 ( = 4860) If mid-points are not given, then no marks except for the following cases:
|
| ÷ 70 | m1 | |
| = 69.4(2…) (cm) | A1 | FT Accept 69 (cm) from correct working. |
| Scheme | Marks | Comments |
|---|---|---|
| No indicated or clearly implied and a suitable explanation e.g. ‘The median is in the group \(65 \leqslant l \lt 70\).’ ‘The median is the 35th (or 35.5th) term and in the group \(65 \leqslant l \lt 70\).’ | B1 | Allow ‘No’ with an explanation e.g. ‘(In group) 65 – 70’ Do not allow ‘No’ and explanation based on 69(.42) or ‘their 69(.42)’ e.g. 69 is not between 70 and 75 (use of mean) or ‘70 to 75 is the modal length’ |
| (5) |