Which one of the following statement is not correct

Options

A. Median divides distributions in two equal subgrops
B. The third quartile is the same as the `75^(th)` percentile
C. The `5^(th)` decile is the same as the `50^(th)` percentile
D. The `50^(th)` decile is the same as the `5^(th)` percentile

Answer

To determine which statement is not correct, we need to analyze each option related to the concepts of mean, median, quartiles, deciles, and percentiles.

### Step-by-step Solution:

1. **Understanding the Definitions**:
- **Median**: The median is the middle value of a data set when it is ordered. It divides the data into two equal parts.
- **Quartiles**:
- The **first quartile (Q1)** is the 25th percentile.
- The **second quartile (Q2)** is the 50th percentile, which is also the median.
- The **third quartile (Q3)** is the 75th percentile.
- **Deciles**:
- The **fifth decile (D5)** is the 50th percentile, which is the same as the median.
- **Percentiles**: Percentiles divide the data into 100 equal parts.

2. **Analyzing Each Statement**:
- **Option A**: "Median divides distribution into two equal subgroups."
- This statement is correct because the median indeed divides the data into two equal halves.
- **Option B**: "The 5th decile is the same as the 50th decile."
- This statement is correct because the 5th decile (D5) is the same as the median (50th percentile).
- **Option C**: "The 3rd quartile is the same as that of the 75th percentile."
- This statement is correct because the 3rd quartile (Q3) is defined as the 75th percentile.
- **Option D**: "The 50th decile is the same as the 5th percentile."
- This statement is incorrect because the 50th decile (D5) is the same as the median (or 50th percentile), not the 5th percentile.

3. **Conclusion**:
- The statement that is not correct is **Option D**: "The 50th decile is the same as the 5th percentile."

### Final Answer:
**Option D** is the incorrect statement.

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