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

Answer

To find the mean of 25 numbers when 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. The formula for mean is:

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

So, we can express the sum of the first 15 numbers as:

\[ \text{Sum of first 15 numbers} = \text{Mean} \times \text{Number of observations} = 18 \times 15 \]

Calculating this gives:

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

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

\[ \text{Sum of remaining 10 numbers} = \text{Mean} \times \text{Number of observations} = 13 \times 10 \]

Calculating this gives:

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

### 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 from the first 15 numbers and the remaining 10 numbers:

\[ \text{Total Sum} = \text{Sum of first 15 numbers} + \text{Sum of remaining 10 numbers} = 270 + 130 \]

Calculating this gives:

\[ \text{Total Sum} = 400 \]

### Step 4: Calculate the mean of all 25 numbers.
Finally, we can find the mean of all 25 numbers using the total sum and the total number of observations:

\[ \text{Mean of all 25 numbers} = \frac{\text{Total Sum}}{\text{Total Number of observations}} = \frac{400}{25} \]

Calculating this gives:

\[ \text{Mean of all 25 numbers} = 16 \]

### Final Answer:
The mean of the 25 numbers is **16**.

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