What is the arithmetic mean of 31, 64, 18, 52, 97, 40, 61, 85?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 56
The arithmetic mean is the sum of the values divided by the number of values.
Sum \(=31+64+18+52+97+40+61+85=448\)
Number of values \(=8\)
Mean \(=448\div8=56\)
The arithmetic mean is 56.
Why the other options are incorrect
Option (2) 57.5 — Incorrect. This is the average of the smallest and largest values, \((18+97)\div2\), not the mean of all eight.
Option (3) 64 — Incorrect. This divides the sum 448 by 7 instead of by 8.
Option (4) 56.5 — Incorrect. This is the median (the middle value in order), not the mean.