The table shows the number of children per family... | WAEC SSCE - General Mathematics - 2009 (Essay)

Question 1 Report

The table shows the number of children per family in a community.

No of children	0	1	2	3	4	5
No of families	3	5	7	4	3	2

(a) Find the : (i) mode ; (ii) third quartile ; (iii) probability that a family has at least 2 children.

(b) If a pie chart were to be drawn for the data, what would be the sectorial angle representing families with one child?

Answer

Total number of families:

\[N=3+5+7+4+3+2=24.\]

Number of children, \(x\)	0	1	2	3	4	5
Number of families, \(f\)	3	5	7	4	3	2
Cumulative frequency	3	8	15	19	22	24

(a)(i) Mode

The greatest frequency is \(7\), which corresponds to 2 children.

\[\boxed{\text{Mode}=2}\]

(a)(ii) Third quartile

\[Q_3=\frac{3}{4}\times24=18.\]

The 18th observation lies between cumulative frequencies 15 and 19, corresponding to 3 children.

\[\boxed{Q_3=3}\]

(a)(iii) Probability of at least 2 children

\[P(X\geq2)=\frac{7+4+3+2}{24}=\frac{16}{24}=\boxed{\frac{2}{3}}.\]

(b) Pie chart

The sector angle for each category is \(\dfrac{f}{24}\times360^\circ\). The completed pie chart is shown below.

graph — Pie chart sectors: 0 children = 45°, 1 child = 75°, 2 children = 105°, 3 children = 60°, 4 children = 45°, 5 children = 30°.

For families with one child:

\[\frac{5}{24}\times360^\circ=\boxed{75^\circ}.\]

Read lesson note on Probability (WAEC)

Read lesson note on Measures Of Location (JAMB)

Read lesson note on Statistics (WAEC)

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