The A.M. of set of 50 numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of number is

Options

A. 38.5
B. 37.5
C. 36.5
D. `36.0`

Answer

To solve the problem step by step, we will follow the logical sequence as described in the video transcript.

### Step 1: Calculate the Sum of the Original Set of Numbers
Given that the Arithmetic Mean (A.M.) of the set of 50 numbers is 38, we can calculate the total sum of these numbers.

\[ \text{Sum of 50 numbers} = \text{Number of items} \times \text{A.M.} = 50 \times 38 = 1900 \]

### Step 2: Calculate the Sum of the Discarded Numbers
Next, we need to find the sum of the two numbers that are discarded, which are 55 and 45.

\[ \text{Sum of discarded numbers} = 55 + 45 = 100 \]

### Step 3: Calculate the Sum of the Remaining Numbers
Now, we will find the sum of the remaining numbers after discarding the two numbers.

\[ \text{Sum of remaining numbers} = \text{Sum of 50 numbers} - \text{Sum of discarded numbers} = 1900 - 100 = 1800 \]

### Step 4: Calculate the New A.M. of the Remaining Set
Since we have discarded 2 numbers from the original set of 50, the number of remaining numbers is:

\[ \text{Number of remaining numbers} = 50 - 2 = 48 \]

Now we can calculate the new A.M. of the remaining set.

\[ \text{New A.M.} = \frac{\text{Sum of remaining numbers}}{\text{Number of remaining numbers}} = \frac{1800}{48} \]

Calculating this gives:

\[ \text{New A.M.} = 37.5 \]

### Final Answer
The A.M. of the remaining set of numbers is **37.5**.

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