The average of 50 number is 36. If two nmumbers, namely 63 and 65 are discarded, the average of the remaining numbers is (Correct to two decimal places)

Options

A. 34.83
B. `32.50`
C. 33.75
D. `36.50`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total sum of the 50 numbers.
The average of the 50 numbers is given as 36. The total sum can be calculated using the formula for average:

\[ \text{Total Sum} = \text{Average} \times \text{Number of Items} \]

Substituting the values:

\[ \text{Total Sum} = 36 \times 50 = 1800 \]

### Step 2: Calculate the sum of the two discarded numbers.
The two numbers that are discarded are 63 and 65. We need to find their sum:

\[ \text{Sum of discarded numbers} = 63 + 65 = 128 \]

### Step 3: Calculate the new total sum after discarding the two numbers.
Now, we subtract the sum of the discarded numbers from the total sum:

\[ \text{New Total Sum} = 1800 - 128 = 1672 \]

### Step 4: Calculate the number of remaining numbers.
After discarding 2 numbers from the original 50, the number of remaining numbers is:

\[ \text{Remaining Numbers} = 50 - 2 = 48 \]

### Step 5: Calculate the new average.
Now we can find the new average by dividing the new total sum by the number of remaining numbers:

\[ \text{New Average} = \frac{\text{New Total Sum}}{\text{Remaining Numbers}} = \frac{1672}{48} \]

Calculating this gives:

\[ \text{New Average} = 34.8333... \]

Rounding this to two decimal places, we get:

\[ \text{New Average} \approx 34.83 \]

### Final Answer:
The average of the remaining numbers, correct to two decimal places, is **34.83**.

---