If the difference between the mode and median is 2 , the difference between the median and mean is `"__________"` (in the given order ) .

Options

A. 2
B. 4
C. 1
D. 0

Explanation

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understand the Given Information:**
We are given that the difference between the mode and the median is 2. This can be expressed mathematically as:
\[ \text{Mode} - \text{Median} = 2 \]

2. **Use the Relationship Between Mode, Median, and Mean:**
There is a known relationship in statistics that relates mode, median, and mean:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

3. **Substitute the Mode in the Relationship:**
From the first step, we can express the mode in terms of the median:
\[ \text{Mode} = \text{Median} + 2 \]
Now, substitute this expression for mode into the relationship:
\[ \text{Median} + 2 = 3 \times \text{Median} - 2 \times \text{Mean} \]

4. **Rearranging the Equation:**
Rearranging the equation gives us:
\[ 2 = 3 \times \text{Median} - \text{Median} - 2 \times \text{Mean} \]
Simplifying this results in:
\[ 2 = 2 \times \text{Median} - 2 \times \text{Mean} \]

5. **Factor Out the Common Terms:**
We can factor out the 2 from the right side:
\[ 2 = 2 \times (\text{Median} - \text{Mean}) \]

6. **Divide Both Sides by 2:**
Dividing both sides by 2 gives:
\[ 1 = \text{Median} - \text{Mean} \]

7. **Final Result:**
Therefore, the difference between the median and the mean is:
\[ \text{Median} - \text{Mean} = 1 \]

### Conclusion:
The difference between the median and the mean is **1**.