| Date | May 2010 | Marks available | 3 | Reference code | 10M.1.sl.TZ1.9 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Complete | Question number | 9 | Adapted from | N/A |
Question
120 Mathematics students in a school sat an examination. Their scores (given as a percentage) were summarized on a cumulative frequency diagram. This diagram is given below.
Complete the grouped frequency table for the students.
Write down the mid-interval value of the \(40 < x \leqslant 60\) interval.
Calculate an estimate of the mean examination score of the students.
Markscheme
(A1)(A1)(A1) (C3)
[3 marks]
50 (A1) (C1)
[1 mark]
\({\text{Mean}} = \frac{{10 \times 14 + ....... + 90 \times 6}}{{120}}\) (M1)
Note: Award (M1) for correct substitution of their values from (a) in mean formula.
\( = 45\frac{2}{3}(45.7)\) (A1)(ft) (C2)
[2 marks]
Examiners report
This question was poorly answered by many of the candidates. A number of students could not identify the specified frequencies from the graph in part a). Most could not give the midinterval value although surprisingly many of these candidates then went on and used the correct mid-interval value in the mean formula. A number did not understand the meaning of ‘an estimate of the mean’ and just wrote down a number read from the diagram.
This question was poorly answered by many of the candidates. A number of students could not identify the specified frequencies from the graph in part a). Most could not give the midinterval value although surprisingly many of these candidates then went on and used the correct mid-interval value in the mean formula. A number did not understand the meaning of ‘an estimate of the mean’ and just wrote down a number read from the diagram.
This question was poorly answered by many of the candidates. A number of students could not identify the specified frequencies from the graph in part a). Most could not give the midinterval value although surprisingly many of these candidates then went on and used the correct mid-interval value in the mean formula. A number did not understand the meaning of ‘an estimate of the mean’ and just wrote down a number read from the diagram.
