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.

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:

Verification / 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