The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, the aver- age of the remaining numbers is :Select one:a. 32.5b. 37.5c. 35d. 36

1. Break Down the Problem

We need to find the average of the remaining numbers after discarding two numbers (45 and 55) from a total of 50 numbers whose current average is 38.

2. Relevant Concepts

The average (mean) of a set of numbers is calculated using the formula: $\text{Average} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}}$ Let's denote:

• Total number of numbers = 50
• Current average = 38
• Numbers to discard = 45, 55

3. Analysis and Detail

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

2. Calculate the sum after discarding the two numbers: $\text{Sum after discarding} = \text{Current Sum} - (\text{Number 1} + \text{Number 2}) = 1900 - (45 + 55)$ $= 1900 - 100 = 1800$

3. Calculate the new total number of numbers: $\text{New total} = 50 - 2 = 48$

4. Calculate the new average: $\text{New Average} = \frac{\text{New Sum}}{\text{New Total}} = \frac{1800}{48}$

4. Verify and Summarize

Now, we perform the division: $1800 \div 48 = 37.5$

Final Answer

The average of the remaining numbers after discarding 45 and 55 is 37.5 (Option b).