4MA0 Foundation June 2013 Paper 2R Q17
17 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 |
(a) Work out the median number of letters in the first names of the 50 people. (2)
(b)
(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.
(4)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.
| Scheme | Marks |
|---|---|
\(\dfrac{50}{2}\) or 25 or \(\dfrac{51}{2}\) or 25.5 or list of all scores | M1 |
| 6 | A1 |
| (2) |
Notes
A1: cao
| Scheme | Marks |
|---|---|
| (i) \(3 \times 2 + 4 \times 5 + 5 \times 14 + 6 \times 19 + 7 \times 10\) 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 1 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 (b)(i)