A joint family consists of two grandparents, two parents, and 4 grandchildren. The average age of the grandparents is 70 years and that of the parents and grandchildren is 50 years and 16 years respectively. What is the average age of the whole family?.

Appeared in: PGIMER Chandigarh NO - 2015

Explanation

The average age is found by dividing the sum of the ages of all family members by the total number of family members.
First, calculate the total age for each group: Grandparents (2 × 70 = 140), Parents (2 × 50 = 100), and Grandchildren (4 × 16 = 64).
The sum of all ages is 140 + 100 + 64 = 304 years.
The total number of family members is 2 + 2 + 4 = 8.
Therefore, the average age of the family is 304 ÷ 8 = 38 years.

Option A: This value is incorrect and likely results from a miscalculation, such as an error in multiplication or addition of the total ages.
Option B: This value is incorrect. A common mistake is to average the group averages (70, 50, 16) without weighting them by the number of people in each group, which would also lead to an incorrect result.
Option D: This value is incorrect and represents a calculation error. It is essential to perform each step of the calculation accurately to arrive at the correct weighted average.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating a weighted average from grouped data as background academic context rather than a clinical decision trigger.
While this is a mathematics question, the underlying skill of performing accurate, multi-step calculations is fundamental in nursing.
Nurses use similar analytical skills for calculating drug dosages based on patient weight, determining IV drip rates, and interpreting quantitative data from lab reports.
Precision in calculation is a critical patient safety competency, as errors can have serious clinical consequences.

How to Approach the Question

Identify the question's goal: The task is to find the average age of the entire family.
Recognize the concept: This is a weighted average problem because the groups (grandparents, parents, grandchildren) have different numbers of members.
Step 1: For each group, multiply the number of people by their average age to find the total age for that group.
Step 2: Sum the total ages from all groups to get the grand total age for the entire family.
Step 3: Sum the number of people in all groups to find the total number of family members.
Step 4: Divide the grand total age by the total number of family members to calculate the final average age.

Concept Tested & Keywords

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