The table below shows the frequency distribution... | WAEC SSCE - General Mathematics - 1993 (Essay)

Question 1 Report

The table below shows the frequency distribution of the marks scored by fifty students in an examination.

Marks (%)	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99
Freq	2	3	4	6	13	10	5	3	2	2

(a) Draw the cumulative frequency curve for the distribution.

(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.

Answer

(a) Cumulative frequency table

Marks (%)	Upper class boundary	Frequency	Cumulative frequency
0–9	9.5	2	2
10–19	19.5	3	5
20–29	29.5	4	9
30–39	39.5	6	15
40–49	49.5	13	28
50–59	59.5	10	38
60–69	69.5	5	43
70–79	79.5	3	46
80–89	89.5	2	48
90–99	99.5	2	50

Plot the cumulative frequencies against the upper class boundaries, beginning with \\((-0.5,0)\\), and join the points with a smooth increasing curve.

graph — Ogive plotted from the upper class boundaries and their cumulative frequencies.

(b)(i) Upper quartile

\[\frac{3N}{4}=\frac{3(50)}{4}=37.5.\]

From the curve, the mark corresponding to cumulative frequency \(37.5\) is approximately \(57\).

\[\boxed{Q_3\approx57\text{ marks}}\]

(b)(ii) Pass mark when 60% passed

Number who passed \(=0.60\times50=30\). Hence the number below the pass mark is \(50-30=20\).

From the curve, the mark corresponding to cumulative frequency \(20\) is approximately \(42\).

\[\boxed{\text{Pass mark}\approx42\text{ marks}}\]

Read lesson note on Inequalities (JAMB)

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