In any discrete series (when all values are not sume) if x represents mean deviation about mean and y represents standard deviation, then which one of the following is correct?

Options

A. `y le x `
B. `y le x`
C. `x=y`
D. `x lt y`

Answer

To solve the problem, we need to analyze the relationship between the mean deviation (x) and the standard deviation (y) in a discrete series.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Mean Deviation (x) is the average of the absolute deviations of each data point from the mean.
- Standard Deviation (y) is a measure of the amount of variation or dispersion in a set of values.

2. **Known Relationship**:
- There is a known statistical result that states:
\[ \text{Mean Deviation} = \frac{4}{5} \times \text{Standard Deviation} \]
- This means that the mean deviation is always a fraction of the standard deviation.

3. **Express the Relationship**:
- From the above relationship, we can express it mathematically as:
\[ x = \frac{4}{5}y \]
- This indicates that mean deviation (x) is less than the standard deviation (y).

4. **Compare x and y**:
- Since \( x = \frac{4}{5}y \), it follows that:
\[ x < y \]
- This confirms that the mean deviation is less than the standard deviation.

5. **Choose the Correct Option**:
- Given the options:
1. \( y \leq x \)
2. \( x = y \)
3. \( x < y \)
4. \( x < y \)
- The correct option is:
- **Option 4: \( x < y \)**.

### Final Answer:
The correct option is **Option 4: \( x < y \)**.