The average of 10 numbers was calculated as 15. Later it was found that one value 36 was wrongly read as 26. What is the correct average of the 10 numbers?

Introduction:
This problem checks error correction in averages. When one observed value is misread, we adjust the total sum by the difference between the correct and incorrect readings, then recompute the average using the same count of observations.

Given Data / Assumptions:

• n = 10 numbers
• Originally computed average = 15 → original computed sum = 15 * 10 = 150
• Misread: 36 was read as 26 (under-recorded by 10)

Concept / Approach:
Correct sum = computed sum + (true value - misread value) = 150 + (36 - 26) = 160. Then correct average = 160 / 10.

Step-by-Step Solution:

Verification / Alternative check:
Replace the misread 26 with 36 in any concrete 10-number set that produces the same initial average; the average rises by 1 exactly because +10 spread across 10 items adds +1 to the average.

Why Other Options Are Wrong:
14, 12.4, 18.6, and 15.5 do not reflect the exact +10 adjustment distributed over 10 items.

Common Pitfalls:
Dividing the correction by 9 or adding 10 directly to the average. Always adjust the sum first, then divide by the original count.

Final Answer:
16