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...
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 Details
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.
For families with one child:
\[\frac{5}{24}\times360^\circ=\boxed{75^\circ}.\]
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