Out of 25 numbers, the mean of 15 numbers is 36 and the mean of the remaining numbers is 26, find the mean of all the 25 numbers.

Answer

To find the mean of all 25 numbers given the mean of two groups of numbers, we can follow these steps:

### Step 1: Calculate the sum of the first 15 numbers.
We know that the mean of the first 15 numbers is 36. The formula for the sum when the mean is given is:

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

Thus, for the first 15 numbers:

\[ \text{Sum of first 15 numbers} = 36 \times 15 = 540 \]

### Step 2: Calculate the sum of the remaining 10 numbers.
The mean of the remaining 10 numbers is given as 26. Using the same formula:

\[ \text{Sum of remaining 10 numbers} = 26 \times 10 = 260 \]

### 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 Step 1 and Step 2:

\[ \text{Total Sum} = \text{Sum of first 15 numbers} + \text{Sum of remaining 10 numbers} \]
\[ \text{Total Sum} = 540 + 260 = 800 \]

### 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:

\[ \text{Mean of all 25 numbers} = \frac{\text{Total Sum}}{\text{Total Number of observations}} = \frac{800}{25} \]

Calculating this gives:

\[ \text{Mean of all 25 numbers} = 32 \]

### Final Answer:
The mean of all 25 numbers is **32**.

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