4MA0 Higher June 2013 Paper 4R Q3
3 The table shows information about the number of letters in the first name of each of 50 people.
| Number of letters | Frequency |
|---|---|
| 3 | 2 |
| 4 | 5 |
| 5 | 14 |
| 6 | 19 |
| 7 | 10 |
(i) Work out the mean number of letters in the first names of the 50 people.
(ii) One more person joins the 50 people.
The mean number of letters in the first names of the 51 people is less than the mean number of letters in the first names of the 50 people.
Write down the greatest number of letters in the first name of the person who joins the group.
The mean number of letters in the first names of the 51 people is less than the mean number of letters in the first names of the 50 people.
Write down the greatest number of letters in the first name of the person who joins the group.
(4)
| Scheme | Marks |
|---|---|
| (i) 3 × 2 + 4 × 5 + 5 × 14 + 6 × 19 + 7 × 10 or 6 + 20 + 70 + 114 + 70 or 280 | M1 |
| “280” ÷ 50 | M1 |
| 5.6 | A1 |
| (ii) 5 | B1 |
| (4) |
Notes
M1: for sum of products condone one error
M1: (dep) for division by 50
A1: cao Also accept 6 if both method marks scored and 5 following 5.6
B1: ft from their (i)