4MA0 Foundation January 2012 Paper 1 Q19
19 The table shows information about the numbers of text messages sent by 40 teenagers in one day.
| Number of text messages | Number of teenagers | Mid-interval value | |
|---|---|---|---|
| 0 to 2 | 3 | 1 | |
| 3 to 5 | 6 | 4 | |
| 6 to 8 | 10 | ||
| 9 to 11 | 15 | ||
| 12 to 14 | 5 | ||
| 15 to 17 | 1 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean number of texts sent by the 40 teenagers in one day. (4)
| Scheme | Marks |
|---|---|
| 9 to 11 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (1 × 3) + (4 × 6) + (7 × 10) + (10 × 15) + (13 × 5) + (16 × 1) (=328) | M2 |
| “328” ÷ (“3 + 6 + 10 + 15 + 5 + 1”) | M1 |
| 8.2 | A1 |
| (4) | |
| (Total 5 marks) |
Notes
M2: All products, \(t \times f\) using ½ way points correctly, and intention to add.
Award M1 if all products, \(t \times f\) using their ½ way points consistently, from 6 to 8 interval onwards and intention to add.
M1: (dep on at least one M1)
A1: Accept 8 with working. 8 without working = M0A0