The following table shows the distribution of test... | WAEC SSCE - General Mathematics - 2006 (Essay)

Question 1 Report

The following table shows the distribution of test scores in a class.

Scores	1	2	3	4	5	7	8	9	10
No of pupils	1	1	5	3	\(k^{2} + 1\)	6	2	3	4

(a) If the mean score of the class is 6, find the : (i) value of k (ii) median score.

(b) Draw a bar chart for the distribution.

Answer

(a)(i) Finding the value of \(k\)

Score, \(x\)	1	2	3	4	5	7	8	9	10	Total
Frequency, \(f\)	1	1	5	3	\(k^2+1\)	6	2	3	4	\(k^2+26\)
\(fx\)	1	2	15	12	\(5k^2+5\)	42	16	27	40	\(5k^2+160\)

Since the mean score is 6,

\[6=\frac{5k^2+160}{k^2+26}\]

\[6k^2+156=5k^2+160\]

\[k^2=4\]

\[\therefore k=2\]

Thus, the frequency for score 5 is \(k^2+1=5\), and the total number of pupils is \(4+26=30\).

(a)(ii) Median score

Score	1	2	3	4	5	7	8	9	10
Cumulative frequency	1	2	7	10	15	21	23	26	30

There are 30 scores. The 15th score is 5 and the 16th score is 7.

\[\text{Median}=\frac{5+7}{2}=6\]

(b) Bar chart of the distribution

graph — Bar chart showing the number of pupils at each score.

(c) Probability of scoring less than 6

The scores less than 6 are 1, 2, 3, 4 and 5.

\[\text{Number of such pupils}=1+1+5+3+5=15\]

\[P(\text{score less than }6)=\frac{15}{30}=\boxed{\frac{1}{2}}\]

Read lesson note on Probability (WAEC)

Read lesson note on Linear Inequalities (WAEC)

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