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 "Which of the following in case of discrete data, is not equal to the median?", we will follow these steps:

### Step 1: Understand the Definition of Median
The median is defined as the middle value of a dataset when it is ordered from least to greatest. In terms of percentiles and quartiles, the median is the 50th percentile, the second quartile (Q2), and the 5th decile.

**Hint:** Remember that the median divides the dataset into two equal halves.

### Step 2: Identify Related Terms
We need to identify terms related to the median:
- **Second Quartile (Q2)**: This is the median itself.
- **15th Percentile**: This is the value below which 15% of the data falls, which is not equal to the median.
- **5th Decile**: This is also the median (50th percentile).
- **Lower Quartile (Q1)**: This is the median of the lower half of the dataset and is less than the median.

**Hint:** Quartiles divide the dataset into four equal parts, while percentiles divide it into 100 parts.

### Step 3: Determine Which is Not Equal to the Median
From the definitions:
- The second quartile (Q2), 5th decile, and 15th percentile are not equal to the median.
- The lower quartile (Q1) is also not equal to the median since it represents the median of the lower half of the dataset.

**Hint:** Compare each term to the definition of the median to see if they are equal.

### Step 4: Conclusion
Among the options provided, the term that is not equal to the median is the **Lower Quartile (Q1)**. Hence, the correct answer is the lower quartile.

**Final Answer:** The lower quartile is not equal to the median.