The average of 50 numbers is 38. If the two numbers 45 and 55 are not considered, what will be the average of remaining numbers?

Options

A. 36.5
B. 37
C. 37.5
D. 37.52

Answer

To find the average of the remaining numbers after excluding 45 and 55 from the original set of 50 numbers, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Sum of the Original 50 Numbers:**
The average of the 50 numbers is given as 38. The formula for average is:
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Total number of observations}} \]
Rearranging this gives us:
\[ \text{Sum of numbers} = \text{Average} \times \text{Total number of observations} \]
Substituting the values:
\[ \text{Sum of numbers} = 38 \times 50 = 1900 \]

2. **Subtract the Excluded Numbers from the Total Sum:**
We need to exclude the numbers 45 and 55 from the total sum. First, calculate the sum of the excluded numbers:
\[ \text{Sum of excluded numbers} = 45 + 55 = 100 \]
Now, subtract this from the total sum:
\[ \text{New Sum} = 1900 - 100 = 1800 \]

3. **Calculate the New Average:**
After excluding the two numbers, the total number of remaining observations is:
\[ 50 - 2 = 48 \]
Now, we can find the new average:
\[ \text{New Average} = \frac{\text{New Sum}}{\text{Total number of remaining observations}} = \frac{1800}{48} \]
Performing the division:
\[ \text{New Average} = 37.5 \]

### Final Answer:
The average of the remaining 48 numbers is **37.5**.