Question

Semi inter-quartile range is given by

• A. $\frac{Q_3 + Q_1}{2}$
• B. $\frac{Q_3 - Q_1}{2}$
• C. $Q_3 - Q_1$
• D. $\frac{Q_3 - Q_1}{4}$

Hint:

Remember: "Semi" means half, so the "semi" inter-quartile range is simply the inter-quartile range divided by 2.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Quartiles partition a sorted dataset into four equal parts.
The dispersion of the middle $50\%$ of the data is measured using quartile differences.

Step 2: Detailed Explanation:
Let us review the definitions of quartile-based measures of dispersion:
- Inter-quartile range (IQR): The absolute difference between the third quartile ($Q_3$) and the first quartile ($Q_1$):
\[ \text{IQR} = Q_3 - Q_1 \]
- Semi inter-quartile range (also widely known as the Quartile Deviation): It is half of the inter-quartile range:
\[ \text{Semi IQR} = \frac{Q_3 - Q_1}{2} \]
Therefore, the semi inter-quartile range is mathematically expressed as $\frac{Q_3 - Q_1}{2}$.

Step 3: Final Answer
The correct option is (B).