4MA0 Foundation January 2016 Paper 2R Q20
20 Mr Rowland has a class of 30 students.
He gave them 24 words to spell.
The table shows information about the number of correct spellings for each student.
| Number of correct spellings | Frequency |
|---|---|
| 0 – 4 | 1 |
| 5 – 9 | 5 |
| 10 – 14 | 6 |
| 15 – 19 | 10 |
| 20 – 24 | 8 |
(a) Write down the modal class. (1)
(b) Work out an estimate for the mean number of correct spellings.
Give your answer to 1 decimal place. (4)
Give your answer to 1 decimal place. (4)
| Scheme | Marks |
|---|---|
| 15 - 19 | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| 2 × 1 + 7 × 5 + 12 × 6 + 17 × 10 + 22 × 8 or 2 + 35 + 72 + 170 + 176 or 455 | M2 |
\(\dfrac{2 \times 1 + 7 \times 5 + 12 \times 6 + 17 \times 10 + 22 \times 8}{30}\) or “455” ÷ 30 | M1 |
| 15.2 | A1 |
| (4) | |
| Total 5 marks |
Notes
M2: Freq × midpoint values stated or evaluated with intention to add (condone any two errors in midpoints or frequencies).
If not M2 then award M1 for all products \(t \times f\) (and \(t\) is consistently within the interval, including end values) and intention to add (condone two errors).
M1: (dep on at least M1) for division by 30
A1: accept 15.166… rounded or truncated to 4 or more sig figs
Accept 15 with working
(15 without working gains M0A0)
NB: accept 2.25 as mid-point for mid-interval value of 1st class (gives mean 15.175)