4MA0 Higher January 2012 Paper 3 Q7
7 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)
(i) Work out an estimate for the mean number of texts sent by the 40 teenagers in one day.
(ii) Explain why your answer to part (b)(i) is an estimate.
(5)| Scheme | Marks |
|---|---|
| 9 to 11 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| (i) (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 |
| (ii) Mid-points used as actual data is unknown | B1 |
| (5) | |
| (Total 6 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 one at least M1)
A1: Accept 8 with working. 8 without working = M0A0
B1: Mention of mid-points or exact (actual) data is unknown.