Question

If the first quartile is 142 and the semi-interquartile range is 18, then the third quartile is:

• A. \(160\)
• B. \(124\)
• C. \(178\)
• D. \(151\)

Hint:

Use \[ Q_3 = Q_1+2(\text{Quartile Deviation}). \] Thus, \[ Q_3 = 142+2(18) = 178. \]

Answer 1

The Correct Option is C

Concept: The interquartile range is \[ Q_3-Q_1, \] and the semi-interquartile range (quartile deviation) is \[ \frac{Q_3-Q_1}{2}. \]

Step 1: Use the given information. Given, \[ Q_1=142 \] and \[ \frac{Q_3-Q_1}{2}=18. \] Therefore, \[ \frac{Q_3-142}{2}=18. \]

Step 2: Solve for \(Q_3\). Multiplying by \(2\), \[ Q_3-142=36. \] Adding \(142\) to both sides, \[ Q_3=178. \] Conclusion: \[ \boxed{178} \] Hence, the correct answer is Option (C).