Theory question 107
Measures of Central TendencyThe table shows the ages of 20 children in a household.
Age: 5, 6, 7, 8, 9, 10
Frequency: 2, 2x − 1, y + 2, 4, 2, y − 1
Given that x : y = 1 : 2, find the (a) values of x and y; (b) mean age of the children.
Show the model answer
Model answer
(a) Σf = 8 + 2x + 2y = 20 ⇒ x + y = 6; y = 2x ⇒ 3x = 6 ⇒ x = 2, y = 4
(b) Frequencies 2, 3, 6, 4, 2, 3; Σfx = 10 + 18 + 42 + 32 + 18 + 30 = 150
Mean age = 150/20 = 7.5 years
Explanation
Use the total frequency of 20 to form the first equation.