The relation between `Q_(3) and P_(75)` is

Options

A. (a)`Q_(3) lt P_(75)`
B. (b)`Q_(3) = P_(75)`
C. (c)`Q_(3) = P_(25)`
D. (d)`Q_(3) ne P_(75)`

Answer

To find the relation between \( Q_3 \) (the third quartile) and \( P_{75} \) (the 75th percentile), we can follow these steps:

### Step 1: Understand the Definitions
- **Quartiles** divide a dataset into four equal parts. The third quartile, \( Q_3 \), is the value below which 75% of the data falls.
- **Percentiles** divide a dataset into 100 equal parts. The 75th percentile, \( P_{75} \), is the value below which 75% of the data falls.

### Step 2: Identify the Relationship
Since both \( Q_3 \) and \( P_{75} \) represent the same position in the dataset (the value below which 75% of the data lies), we can establish their relationship.

### Step 3: State the Conclusion
From the definitions, we can conclude that:
\[ Q_3 = P_{75} \]

### Final Answer
The relation between \( Q_3 \) and \( P_{75} \) is:
\[ Q_3 = P_{75} \]

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