For a certain data, if the median is equal to the mean, then the mode =_________

Answer

To solve the problem, we need to find the value of the mode when the median is equal to the mean. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that the median (M) is equal to the mean (A). So we can write:
\[ M = A \]

2. **Using the Relationship Between Mean, Median, and Mode**:
There is a known relationship in statistics that connects the mean, median, and mode:
\[ 3M = 2A + \text{Mode} \]
Here, we need to find the mode.

3. **Substituting the Values**:
Since we know that \( M = A \), we can substitute \( A \) for \( M \) in the equation:
\[ 3M = 2M + \text{Mode} \]

4. **Rearranging the Equation**:
Now, we can rearrange the equation to isolate the mode:
\[ \text{Mode} = 3M - 2M \]
Simplifying this gives us:
\[ \text{Mode} = M \]

5. **Conclusion**:
Since we established that \( M = A \), we can conclude that:
\[ \text{Mode} = M = A \]
Therefore, the mode is equal to the mean and the median.

### Final Answer:
\[ \text{Mode} = \text{Mean} = \text{Median} \]