Higher November 2022 Paper 2 Q2
2. The table gives a summary of the masses, \(m\) grams, of 30 buzzards.
| Mass, \(m\) (grams) | \(600 \leqslant m \lt 700\) | \(700 \leqslant m \lt 800\) | \(800 \leqslant m \lt 900\) | \(900 \leqslant m \lt 1000\) |
|---|---|---|---|---|
| Frequency | 8 | 7 | 4 | 11 |
(a) Moeen uses the midpoint of each group to calculate an estimate of the mean mass of these buzzards.
He does this correctly.
Calculate Moeen’s answer. [3]
He does this correctly.
Calculate Moeen’s answer. [3]
(b) Deeta decides to estimate the mean mass of these buzzards.
She uses the values 600, 700, 800 and 900 rather than the midpoints.
Explain why her method is unlikely to give a good estimate of the mean mass. [1]
She uses the values 600, 700, 800 and 900 rather than the midpoints.
Explain why her method is unlikely to give a good estimate of the mean mass. [1]
| Scheme | Marks | Comments |
|---|---|---|
| (650 × 8 + 750 × 7 + 850 × 4 + 950 × 11) | M1 | (= 24300) |
| ÷ 30 | m1 | |
| 810 (grams) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| Valid comment e.g. ‘Her answer will be an underestimate.’ ‘She is using the lowest values so the mean will be too small’. | E1 | Allow answers that state that the calculated mean will be smaller or indicate that the lowest values do not represent the groups, e.g. ‘Her method will give a smaller mean.’ ‘Because these values do not represent the entire range.’ ‘Because she ignored the distribution in each interval.’ ‘Because she is using the minimum masses making at an unfair estimate.’ Do not allow e.g. ‘She has used the smallest value in each group.’ ‘Because these values are the lowest bounds.’ ‘Because it is not as accurate as the midpoints.’ ‘It is better to use the midpoints’ |
| (4) |