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?
Explanation
(a) (i) Mode = 2
(ii) Third quartile : Sum of frequency = 24
\(Q_{3} = \frac{3}{4} \times 24 = 18\)
The 18th position falls at 3.
(iii) P(at least 2 children) = \(\frac{7 + 4 + 3 + 2}{24}\)
= \(\frac{16}{24}\)
= \(\frac{2}{3}\)
(b) The sector for 1 child = \(\frac{5}{24} \times 360\)
= \(75°\).