The arithmetic mean of a set of 50 numbers is 38. If two numbers of the set, namely 60 and 40 discarded, the arithmetic mean of the remaining set of numbers is

Options

A. 38.5
B. 37.5
C. 36.5
D. 36

Answer

To find the new arithmetic mean after discarding two numbers from a set, we can follow these steps:

### Step 1: Calculate the original sum of the numbers.
The arithmetic mean (AM) is given by the formula:
\[ \text{AM} = \frac{\text{Sum of all terms}}{\text{Number of terms}} \]
Given that the arithmetic mean of the 50 numbers is 38, we can calculate the sum of the numbers:
\[ \text{Sum} = \text{AM} \times \text{Number of terms} = 38 \times 50 = 1900 \]

### Step 2: Determine the new sum after discarding the two numbers.
The two numbers being discarded are 60 and 40. Therefore, the total amount removed from the sum is:
\[ \text{Total discarded} = 60 + 40 = 100 \]
Now, we can find the new sum of the remaining numbers:
\[ \text{New Sum} = \text{Original Sum} - \text{Total discarded} = 1900 - 100 = 1800 \]

### Step 3: Calculate the new number of terms.
Since we have discarded 2 numbers from the original set of 50, the new number of terms is:
\[ \text{New Number of terms} = 50 - 2 = 48 \]

### Step 4: Calculate the new arithmetic mean.
Now we can find the new arithmetic mean using the new sum and the new number of terms:
\[ \text{New AM} = \frac{\text{New Sum}}{\text{New Number of terms}} = \frac{1800}{48} \]
Calculating this gives:
\[ \text{New AM} = 37.5 \]

### Final Answer:
The new arithmetic mean of the remaining set of numbers is **37.5**.

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