`Q_(1)` is always equal to :

Options

A. (i) `P_(1)`
B. (ii) `P_(10)`
C. (iii) `P_(25)`
D. (iv) `P_(50)`

Answer

To solve the question regarding the first quartile \( Q_1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Quartiles**:
- Quartiles are values that divide a data set into four equal parts. The first quartile \( Q_1 \) is the value below which 25% of the data falls.

2. **Relating Quartiles to Percentiles**:
- Percentiles are values that divide a rank-ordered data set into 100 equal parts. The first quartile \( Q_1 \) corresponds to the 25th percentile of the data.

3. **Expressing \( Q_1 \)**:
- Since \( Q_1 \) is the first quartile, we can express it mathematically as:
\[ Q_1 = P_{25} \]
- Here, \( P_{25} \) denotes the 25th percentile.

4. **Identifying the Correct Option**:
- Given the options in the question, we can conclude that \( Q_1 \) is always equal to the 25th percentile, which corresponds to option number three.

### Final Answer:
Thus, \( Q_1 \) is always equal to \( P_{25} \).

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