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: All partition values, quartiles, deciles and percentiles, are defined by the same underlying rule: arrange the data in ascending order and locate the value below which a certain percentage of observations fall.

Step 2: The median is defined as the value below which exactly 50% of the observations lie.

Step 3: Check each partition scale for the value that also corresponds to 50%. On the quartile scale ($Q_1, Q_2, Q_3$ correspond to 25%, 50%, 75%), $Q_2$ hits 50%. On the decile scale ($D_1$ through $D_9$ correspond to multiples of 10%), $D_5$ hits 50%. On the percentile scale ($P_1$ through $P_{99}$), $P_{50}$ hits 50%.

Step 4: Since each of these three values, $Q_2$, $D_5$ and $P_{50}$, corresponds to the same 50% cutoff, they are all numerically equal to the median.

\[ \boxed{\text{Quartile, decile and percentile, all the three}} \]