The average of 50 numbers is 38. If two numbers 45 and 55 are discarded, the average of the remaining numbers is:Options :36.53737.537.52

1. Break Down the Problem

To find the new average after discarding the two numbers (45 and 55), we need to:

1. Calculate the total sum of the original 50 numbers.
2. Subtract the sum of the discarded numbers from the total sum.
3. Calculate the average of the remaining numbers.

2. Relevant Concepts

• Average formula: $\text{Average} = \frac{\text{Total Sum}}{\text{Number of Items}}$

3. Analysis and Detail

1. Calculate the total sum of the 50 numbers: $\text{Total Sum} = \text{Average} \times \text{Number of Items} = 38 \times 50$ $\text{Total Sum} = 1900$

2. Calculate the sum of the two discarded numbers: $\text{Sum of Discarded Numbers} = 45 + 55 = 100$

3. Calculate the new total sum after discarding: $\text{New Total Sum} = 1900 - 100 = 1800$

4. Calculate the number of remaining numbers: $\text{Remaining Numbers} = 50 - 2 = 48$

5. Calculate the new average: $\text{New Average} = \frac{\text{New Total Sum}}{\text{Remaining Numbers}} = \frac{1800}{48}$ $\text{New Average} = 37.5$

4. Verify and Summarize

We have completed the calculations, and the average of the remaining numbers after discarding 45 and 55 is confirmed to be 37.5.

Final Answer

The average of the remaining numbers is 37.5.