The average of a list of 7 numbers is 23. If we remove one of the numbers, the average of the remaining numbers is 18. What is the number that was removed?

\$"Sum of Terms" = "Average" \times "Number of Terms"\$

The removed number could be obtained by difference between the sum of original 6 numbers and the sum of remaining 5 numbers i.e.

\$"Removed number = sum of original 6 numbers - sum of remaining 5 numbers"\$

Using the formula

\$"Sum of Terms" = "Average" \times "Number of Terms"\$

sum of original 6 numbers = \$20 \times 6 = 120\$

sum of remaining 5 numbers = \$15 \times 5 = 75\$

Using the formula from step 1

Removed number = sum of original 6 numbers - sum of remaining 5 numbers

⇒ \$120 - 75 = 45\$

The number removed is 45.