If the difference between the mode and median is 2, then the difference between the median and mean is (in the given order)

Options

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

Answer

To solve the problem step by step, we start with the information given in the question.

### Step 1: Understand the relationship between mode, median, and mean.
We know that:
\[ \text{Mode} - \text{Median} = 2 \]
This means:
\[ \text{Mode} = \text{Median} + 2 \]

### Step 2: Use the relationship between mode, median, and mean.
There is a known relationship in statistics:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step 3: Substitute the expression for mode.
Substituting the expression for mode from Step 1 into the relationship from Step 2, we get:
\[ \text{Median} + 2 = 3 \times \text{Median} - 2 \times \text{Mean} \]

### Step 4: Rearrange the equation.
Rearranging the equation gives us:
\[ 2 = 3 \times \text{Median} - \text{Median} - 2 \times \text{Mean} \]
This simplifies to:
\[ 2 = 2 \times \text{Median} - 2 \times \text{Mean} \]

### Step 5: Factor out the common term.
Factoring out 2 from the right side, we have:
\[ 2 = 2 \times (\text{Median} - \text{Mean}) \]

### Step 6: Solve for the difference between median and mean.
Dividing both sides by 2 gives:
\[ 1 = \text{Median} - \text{Mean} \]
Thus, we can conclude:
\[ \text{Median} - \text{Mean} = 1 \]

### Final Result:
The difference between the median and mean is \( 1 \).

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