Find the mean of 25 numbers, if the mean of 15 of them is 18 and the mean of the remaining numbers is 13.

Options

A. 26
B. 44
C. 39
D. 16

Answer

To find the mean of 25 numbers, given that the mean of 15 of them is 18 and the mean of the remaining 10 numbers is 13, we can follow these steps:

### Step 1: Calculate the sum of the first 15 numbers
The mean of the first 15 numbers is given as 18. We can find the sum of these 15 numbers using the formula:

\[ \text{Sum} = \text{Mean} \times \text{Number of observations} \]

So, the sum of the first 15 numbers is:

\[ \text{Sum of 15 numbers} = 18 \times 15 = 270 \]

### Step 2: Calculate the sum of the remaining 10 numbers
The mean of the remaining 10 numbers is given as 13. We can find the sum of these 10 numbers using the same formula:

\[ \text{Sum of 10 numbers} = 13 \times 10 = 130 \]

### Step 3: Calculate the total sum of all 25 numbers
Now, we can find the total sum of all 25 numbers by adding the sums of the two groups:

\[ \text{Total Sum} = \text{Sum of 15 numbers} + \text{Sum of 10 numbers} \]

Substituting the values we calculated:

\[ \text{Total Sum} = 270 + 130 = 400 \]

### Step 4: Calculate the mean of all 25 numbers
Finally, we can find the mean of all 25 numbers using the formula:

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

Substituting the total sum and the number of observations:

\[ \text{Mean} = \frac{400}{25} = 16 \]

Thus, the mean of the 25 numbers is **16**.