Higher June 2024 Paper 2 Q11
11 The frequency table gives information about the weights of 60 parcels.
| Weight (\(w\) kg) | Frequency |
|---|---|
| \(0 \lt w \leqslant 2\) | 7 |
| \(2 \lt w \leqslant 4\) | 21 |
| \(4 \lt w \leqslant 6\) | 15 |
| \(6 \lt w \leqslant 8\) | 11 |
| \(8 \lt w \leqslant 10\) | 6 |
(a) Complete the cumulative frequency table.
(1)
| Weight (\(w\) kg) | Cumulative frequency |
|---|---|
| \(0 \lt w \leqslant 2\) | |
| \(0 \lt w \leqslant 4\) | |
| \(0 \lt w \leqslant 6\) | |
| \(0 \lt w \leqslant 8\) | |
| \(0 \lt w \leqslant 10\) |
(b) On the grid below, draw a cumulative frequency graph for your table.
(2)

(c) Use your graph to find an estimate for the interquartile range. (2)
(d) Use your graph to find an estimate for the number of these parcels with a weight greater than 7.4 kg. (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| 7, 28, 43, 54, 60 | B1 | cao |
| Answer | Mark | Mark scheme |
|---|---|---|
| cf graph | M1 | for 4 or 5 of their points plotted correctly from a cf table |
| A1 | for a fully correct graph SCB1 if 4 or 5 of their points plotted not at the end but consistent within each interval and joined; providing no gradient is negative |
Additional guidance
Ignore any histograms
Ignore anything drawn to the left of the first point
Accept a smooth curve or line segments
| Answer | Mark | Mark scheme |
|---|---|---|
| 3.4 to 4 | M1 | for at least one correct quartile, eg (UQ =) value in the range 6.2 to 6.4 or (LQ =) value in the range 2.6 to 2.8 or ft their cf graph |
| A1 | for answer in the range 3.4 to 4 or ft their cf graph |
Additional guidance
CF graph must have no negative gradient to award ft
| Answer | Mark | Mark scheme |
|---|---|---|
| 7 to 10 | M1 | for cf reading at weight = 7.4 in the range 50 to 53 or ft their cf graph |
| A1 | for answer in the range 7 to 10 or ft their cf graph |
Additional guidance
CF graph must have no negative gradient to award ft