Question

Which can be the median among quartile, decile and percentile?

• A. Only quartile but not decile and percentile
• B. Quartile and decile but not percentile
• C. Decile and percentile but not quartile
• D. Quartile, decile and percentile, all the three

Hint:

Median = 50th percentile = 5th decile = 2nd quartile; all three partition scales agree at the halfway point.

Answer 1

The Correct Option is D

Step 1: The quartiles divide ranked data into 4 equal parts, so the second quartile \(Q_2\) marks the point below which 50% of the data lie, which is exactly the definition of the median.

Step 2: The deciles divide ranked data into 10 equal parts, so the fifth decile \(D_5\) also marks the 50% point of the data, again identical to the median.

Step 3: The percentiles divide ranked data into 100 equal parts, so the fiftieth percentile \(P_{50}\) marks the 50% point as well, identical to the median.

Since \(Q_2 = D_5 = P_{50} = \text{Median}\), the median can be expressed as any of the three positional measures.

The correct answer is (D) Quartile, decile and percentile, all the three.