Question

The mean of $5$ numbers is $24$. If one number is excluded, the mean becomes $20$. What is the excluded number?

• A. $24$
• B. $36$
• C. $40$
• D. $44$

Hint:

If the mean decreases after a number is removed (like going from $24$ to $20$), it means the excluded number was higher than the original mean. This helps you quickly eliminate smaller options!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The "mean" or average is the sum of all values divided by the number of values. To find a missing or excluded number, we can use the relationship: $\text{Sum} = \text{Mean} \times \text{Count}$.

Step 2: Calculating Total Sum of 5 Numbers:
Given the mean of $5$ numbers is $24$: \[ \text{Sum of 5 numbers} = 5 \times 24 = 120 \]

Step 3: Calculating Total Sum of 4 Numbers:
After excluding one number, $4$ numbers remain. Their new mean is $20$: \[ \text{Sum of remaining 4 numbers} = 4 \times 20 = 80 \]

Step 4: Finding the Difference:
The number that was removed is the difference between the original sum and the new sum: \[ \text{Excluded Number} = (\text{Sum of 5 numbers}) - (\text{Sum of 4 numbers}) \] \[ \text{Excluded Number} = 120 - 80 = 40 \]

Step 5: Final Answer:
The excluded number is $40$.