Arrange the following statistical measures in increasing order. (A) Sixth…
2024
Arrange the following statistical measures in increasing order.
(A) Sixth decile
(B) Median
(C) Third quartile
(D) 67th percentile
Choose the correct answer from the options given below :
Answer: C. (B), (A), (D), (C) — ConceptDeciles, percentiles, quartiles, and the median are positional measures on the same cumulative scale. The kth percentile marks k% of observations at or…
- A.
(A), (D), (B), (C)
- B.
(B), (C), (A), (D)
- C.
(B), (A), (D), (C)
- D.
(A), (C), (D), (B)
Show answer & explanation
Correct answer: C
Concept
Deciles, percentiles, quartiles, and the median are positional measures on the same cumulative scale.
The kth percentile marks k% of observations at or below it; therefore D6 = P60, the median = P50, and Q3 = P75.
Application
Measure | Equivalent percentile |
|---|---|
Median | P50 |
Sixth decile | P60 |
67th percentile | P67 |
Third quartile | P75 |
Convert every measure to a percentile: median = P50, sixth decile = P60, 67th percentile = P67, and third quartile = P75.
Compare the percentile ranks: 50 < 60 < 67 < 75.
Map the ranks back to the listed measures: median, sixth decile, 67th percentile, third quartile.
Cross-check
The median divides the ordered data at 50%, a sixth decile lies at 60%, and the third quartile lies at 75%; hence the 67th percentile must lie between the sixth decile and the third quartile.
Thus the increasing order is (B), (A), (D), (C).