4MA0 Foundation January 2015 Paper 2 Q11
11 Becky counted the number of matches in each of 50 boxes.
The table shows information about her results.
| Number of matches | Frequency |
|---|---|
| 45 | 3 |
| 46 | 7 |
| 47 | 12 |
| 48 | 23 |
| 49 | 4 |
| 50 | 1 |
(a) Write down the mode of the number of matches. (1)
(b) Work out the range of the number of matches. (2)
(c) Work out the mean number of matches. (3)
| Scheme | Marks |
|---|---|
| 48 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 50 − 45 | M1 |
| 5 | A1 |
| (2) |
Notes
M1: for 45 and 50 (corrected from the printed mark scheme: “for 35 and 50”)
| Scheme | Marks |
|---|---|
| 45×3 + 46×7 + 47×12 + 48×23 + 49×4 + 50×1 or 135 + 322 + 564 + 1104 + 196 + 50 or 2371 | M1 |
"2371"÷50 or \(\dfrac{45\times3 + 46\times7 + 47\times12 + 48\times23 + 49\times4 + 50(\times1)}{50}\) | M1 |
| 47.42 | A1 |
| (3) | |
| (6 marks) |
Notes
M1: for at least 3 correct products and summing them
M1: (dep) for division by 50
NB. If division by something other than 50 this must clearly come from adding the frequency column
A1: Accept 47, 47.4 if 2371÷50 seen
accept \(47\dfrac{21}{50}\) but not \(\dfrac{2371}{50}\)