Statistics: Exam-Pattern Drill (6)

Question

The mean of $5$ numbers is $20$. If one number is excluded, the mean of the remaining $4$ becomes $18$. Find the excluded number. (CBSE Class 10 boards 2023)

Solution — Step by Step

Final answer: The excluded number is $28$.

Why This Works

Mean problems become trivial when we convert to sums. The mean is just (sum)/(count), so multiplying back gives the sum, and the difference of sums isolates the missing value.

This pattern — “given two means, find the missing item” — is one of CBSE’s most repeated Class 10 boards questions, easily worth $2$ marks.

Alternative Method

Set up equations. Let the five numbers be $x_1, x_2, x_3, x_4, x_5$ with $\sum x_i = 100$. After excluding $x_5$, $x_1 + x_2 + x_3 + x_4 = 72$. So $x_5 = 100 - 72 = 28$. Same logic, more notation.

Common Mistake