What is the mean of the first 15 prime numbers (correct to two decimal places)?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 21.87
List the primes in order starting from 2 (1 is not a prime), add them and divide by how many there are.
First 15 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Sum \(=328\)
Mean \(=328\div15=21.8667\ldots\)
The mean is 21.87.
Why the other options are incorrect
Option (1) 23.43 — Incorrect. This divides the sum 328 by 14 instead of by 15.
Option (3) 25.27 — Incorrect. This leaves out 2, the only even prime, and takes the next 15 primes instead.
Option (4) 18.80 — Incorrect. This counts 1 as a prime; 1 is not a prime, so the first 15 primes run from 2 to 47.