Date | May 2016 | Marks available | 3 | Reference code | 16M.1.sl.TZ2.14 |
Level | SL only | Paper | 1 | Time zone | TZ2 |
Command term | Calculate | Question number | 14 | Adapted from | N/A |
Question
A group of students were asked how long they spend practising mathematics during the week. The results are shown in the following table.
It is known that \(35 < a < 52\) .
Write down
i) the modal class;
ii) the mid-interval value of the modal class;
iii) the class in which the median lies.
For this group of students, the estimated mean number of hours spent practising mathematics is \(2.69\).
Calculate the value of \(a\) .
Markscheme
i) \(3 \leqslant t < 4\) (A1) (C1)
Note: Accept equivalent notation: \([3,\,\,4)\) or \([3,\,\,4[\).
ii) \(3.5\) (A1)(ft) (C1)
Note: Follow through from part (a)(i).
iii) \(2 \leqslant t < 3\) (A1)(ft) (C1)
Note: Follow through from part (a)(i), for consistent misuse of inequality. Accept equivalent notation: \([2,\,\,3)\) or \([2,\,\,3[\).
\(\frac{{3.5 \times 0.5 + 30 \times 1.5 + a \times 2.5 + 52 \times 3.5 + 43 \times 4.5}}{{35 + 30 + a + 52 + 43}} = 2.69\) (M1)(A1)(ft)
Notes: Award (M1) for substitution into mean formula and equating to \(2.69\), (A1)(ft) for correct substitutions. Follow through from their mid-interval value in part (a)(ii).
\((a = )\,\,40\) (A1)(ft) (C3)
Note: The final (A1)(ft) is awarded only if \(a\) is an integer and \(35 < a < 52\). Follow through from part (a)(ii).
Examiners report
Question 14: Grouped frequency table.
Candidates were able to identify the modal class and the class in which the median lies but few were able to find a missing value from the grouped frequency table given the estimated mean.
Question 14: Grouped frequency table.
Candidates were able to identify the modal class and the class in which the median lies but few were able to find a missing value from the grouped frequency table given the estimated mean.