The mean of 15 numbers is 40. If two numbers 45 and 35 are removed, then what will be the mean of meaning numbers?

Options

A. a)`37.5`
B. b)40
C. c)`42.5`
D. d)38

Answer

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

### Step 1: Calculate the Total of the 15 Numbers
Given that the mean of 15 numbers is 40, we can find the total of these numbers using the formula for mean:

\[ \text{Mean} = \frac{\text{Total}}{\text{Number of Observations}} \]

Rearranging this gives us:

\[ \text{Total} = \text{Mean} \times \text{Number of Observations} \]

Substituting the given values:

\[ \text{Total} = 40 \times 15 = 600 \]

### Step 2: Calculate the Sum of the Removed Numbers
Next, we need to find the sum of the two numbers that are removed, which are 45 and 35.

\[ \text{Sum of Removed Numbers} = 45 + 35 = 80 \]

### Step 3: Calculate the New Total After Removal
Now, we subtract the sum of the removed numbers from the original total:

\[ \text{New Total} = 600 - 80 = 520 \]

### Step 4: Calculate the New Number of Observations
After removing 2 numbers from the original 15, the new number of observations is:

\[ \text{New Number of Observations} = 15 - 2 = 13 \]

### Step 5: Calculate the New Mean
Finally, we can find the new mean using the new total and the new number of observations:

\[ \text{New Mean} = \frac{\text{New Total}}{\text{New Number of Observations}} = \frac{520}{13} \]

Calculating this gives us:

\[ \text{New Mean} = 40 \]

### Final Answer
The mean of the remaining numbers after removing 45 and 35 is **40**.

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