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 = \(\frac{5}{24} \times 360\) = \(75°\).
