The table shows the marks scored by a group of students in a class test. Marks 0 1 2 3 4 5 Frequency 1 4 9 8 5 3 (a)(i) Calculate the mean mark ; (ii) Find ...
Question 1 Report
The table shows the marks scored by a group of students in a class test.
| Marks | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 1 | 4 | 9 | 8 | 5 | 3 |
(a)(i) Calculate the mean mark ; (ii) Find the median.
(b) If the information were to be represented in a pie chart, what would be the sectorial angle for the mark 2?
Answer Details
(a) Prepare the frequency table:
| Mark, \(x\) | 0 | 1 | 2 | 3 | 4 | 5 | Total |
|---|---|---|---|---|---|---|---|
| Frequency, \(f\) | 1 | 4 | 9 | 8 | 5 | 3 | 30 |
| \(fx\) | 0 | 4 | 18 | 24 | 20 | 15 | 81 |
| Cumulative frequency | 1 | 5 | 14 | 22 | 27 | 30 |
(i) Mean mark
\[\bar{x}=\frac{\sum fx}{\sum f}=\frac{81}{30}=2.7\]
(ii) Median
There are \(30\) observations. The median lies between the 15th and 16th observations. From the cumulative frequencies, both the 15th and 16th observations have mark \(3\).
\[\text{Median}=3\]
(b) Pie chart
The sector angle for each mark is \(\dfrac{f}{30}\times360^\circ\). Thus, for mark \(2\):
\[\frac{9}{30}\times360^\circ=108^\circ\]
Therefore, the sectorial angle for mark \(2\) is \(108^\circ\).
The complete pie chart is shown below. Its sector angles are \(12^\circ,48^\circ,108^\circ,96^\circ,60^\circ\), and \(36^\circ\) for marks \(0,1,2,3,4\), and \(5\) respectively.
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