Average update after adding observations: The average of 5 observations is 15. Three new observations 16.5, 18, and 14.5 are added. What is the new average of all 8 observations?

Introduction / Context:
This tests recomputing an average after adding additional values.

Given Data / Assumptions:

• Initial count = 5, average = 15
• New observations: 16.5, 18, 14.5

Concept / Approach:
Compute the original total from average * count. Add the sum of the new three values. Divide by the new count (8) to obtain the updated average.

Step-by-Step Solution:
Original total = 5 * 15 = 75Sum of new = 16.5 + 18 + 14.5 = 49New total = 75 + 49 = 124New average = 124 / 8 = 15.5

Verification / Alternative check:
Compute each value's deviation from 15 and average deviations; total deviation is 0.5 per item on average across eight, confirming 15.5.

Why Other Options Are Wrong:
14.8, 16.2, 15.0, 15.6 do not match the exact arithmetic above.

Common Pitfalls:
Using 5 as the divisor after adding three items; forgetting to add all three values correctly.

Final Answer:
15.5