If mode - mean = mean - mode, then which of the following is necessarily true?

Options

A. Mean = Median
B. Median = Mode
C. Mean = Mode
D. All of these

Answer

To solve the problem, we need to analyze the given equation:

**Given:**
Mode - Mean = Mean - Mode

**Step 1: Rearranging the equation**
We can rearrange the equation to group like terms. Let's add Mode to both sides:

Mode - Mean + Mode = Mean - Mode + Mode
This simplifies to:
2 * Mode = Mean

**Step 2: Dividing both sides by 2**
Now, we can divide both sides of the equation by 2:

Mode = Mean / 2

**Step 3: Conclusion**
From the equation we derived (Mode = Mean / 2), we can conclude that the mode is half of the mean. This indicates a specific relationship between the mode and the mean.

**Final Statement:**
Thus, the statement that is necessarily true is that the mode is equal to half the mean.