A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

Given data

• Family members: 2 grandparents, 2 parents, 3 grandchildren (total = 7)
• Average age of grandparents = 67 years ⇒ total for grandparents = 2 × 67 = 134
• Average age of parents = 35 years ⇒ total for parents = 2 × 35 = 70
• Average age of grandchildren = 6 years ⇒ total for grandchildren = 3 × 6 = 18

Step 1: Compute the family's total age
Total age = 134 + 70 + 18 = 222 years

Step 2: Compute the overall average
Average age = Total age ÷ Number of members= 222 ÷ 7 = 31 + 5/7 ≈ 31.71 years

Why weighted averages matter here

• Each subgroup's average must be converted to a sum before combining; directly averaging 67, 35, and 6 would be incorrect because the subgroup sizes differ.
• Always total the subgroup sums, then divide by the total headcount.

Final Answer
The average age of the family is 31.71 years (i.e., 31 5/7 years).