Theory question 103
Measures of Central TendencyThe 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?
Show the model answer
Model answer
Total families = 24.
(a)(i) Mode = 2 children (highest frequency, 7).
(ii) Third quartile = ¾ × 24 = 18th family. Cumulative frequencies 3, 8, 15, 19, …, so the 18th family has 3 children: Q3 = 3.
(iii) At least 2 children: 7 + 4 + 3 + 2 = 16. P = 16/24 = 2/3.
(b) 5/24 × 360° = 75°.
Explanation
Use cumulative frequency to locate the quartile.