Which of the following in case of a discrete data, is not equal to the median?

Options

A. 50 percentile
B. 5th decile
C. 2nd quartile
D. lower quartile

Answer

To solve the question, we need to analyze the definitions of the terms provided and their relationship with the median in the context of discrete data.

### Step-by-Step Solution:

1. **Understanding Median**:
The median is the value that separates the higher half from the lower half of a data sample. For discrete data, it is the 50th percentile, which means that 50% of the data points are below the median.

**Hint**: Remember that the median is the middle value of a sorted dataset.

2. **Identifying Percentiles, Deciles, and Quartiles**:
- **50th Percentile**: This is the median itself. Therefore, it is equal to the median.
- **6th Decile**: The 6th decile corresponds to the 60th percentile. It represents the value below which 60% of the data falls. This is greater than the median (50th percentile) and thus is not equal to the median.
- **2nd Quartile**: The 2nd quartile is also the median. Therefore, it is equal to the median.
- **Lower Quartile (1st Quartile)**: This is the median of the lower half of the dataset. It can be equal to or less than the median, but it is not guaranteed to be equal.

3. **Conclusion**:
Among the options given:
- 50th Percentile = Median
- 6th Decile ≠ Median
- 2nd Quartile = Median
- Lower Quartile ≠ Median (it can be less than or equal to the median)

Therefore, the option that is **not equal to the median** in case of discrete data is the **6th Decile**.

### Final Answer:
The answer is **6th Decile**.