The table shows the marks scored by a group of... | WAEC SSCE - General Mathematics - 2004 (Essay)

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

(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.

graph — Pie chart representing the marks scored by the 30 students. The sector for mark 2 is 108°.

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