Replacement effect on mean: The average of 8 persons increases by 2.5 kg when a 56 kg person is replaced by a new person. Find the weight of the new person.
Correct Answer: 76 kg
Introduction / Context:Replacing one data point changes the total by an amount equal to (new value - old value). If the average rises by a known amount, multiply that by the count to get the change in total, then solve for the new value.
Given Data / Assumptions:
- Count = 8 persons
- Old person weight = 56 kg
- Average increases by 2.5 kg
Concept / Approach:Increase in total = increase in average * count. Then new weight = old weight + increase in total.
Step-by-Step Solution:
Increase in total = 2.5 * 8 = 20 kgNew person weight = 56 + 20 = 76 kgVerification / Alternative check:New total is old total + 20. Dividing by 8 gives the new average which is 2.5 kg higher, confirming the logic.
Why Other Options Are Wrong:
- 66, 75, 78, 86 kg: do not produce the specified rise in mean across 8 persons.
Common Pitfalls:Multiplying the increase by 1 instead of the group size, or subtracting from 56 instead of adding when the average rises.
Final Answer:76 kg