For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find mean for this distribution using an empirical relation

Answer

To find the mean of the distribution using the empirical relation between the mode, median, and mean, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Mode (Mo) = 1000
- Median (Me) = 1250

2. **Use the empirical relation:**
The empirical relation between mode, median, and mean (M) is given by:
\[ 3 \times \text{Median} = \text{Mode} + 2 \times \text{Mean} \]
Rearranging this relation to find the mean gives:
\[ \text{Mean} = \frac{3 \times \text{Median} - \text{Mode}}{2} \]

3. **Substitute the values into the equation:**
Substitute the values of median and mode into the equation:
\[ \text{Mean} = \frac{3 \times 1250 - 1000}{2} \]

4. **Calculate the numerator:**
First, calculate \(3 \times 1250\):
\[ 3 \times 1250 = 3750 \]
Now substitute this back into the equation:
\[ \text{Mean} = \frac{3750 - 1000}{2} \]

5. **Perform the subtraction:**
Now calculate \(3750 - 1000\):
\[ 3750 - 1000 = 2750 \]

6. **Divide by 2:**
Finally, divide by 2 to find the mean:
\[ \text{Mean} = \frac{2750}{2} = 1375 \]

7. **Conclusion:**
Thus, the mean of the distribution is:
\[ \text{Mean} = 1375 \]

### Final Answer:
The mean for this distribution is **1375**.