Given below are two statements: Statement I: A percentile divides the…
2020
Given below are two statements:
Statement I: A percentile divides the distribution into 100 equal parts Statement II: Range is the distribution between zero and highest value
In light of the above statements, choose the most appropriate answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 9 students.
Show answer & explanation
Correct answer: C
Concept
This item tests two definitions from descriptive statistics. Percentiles are positional partition values: they are the 99 points that split rank-ordered data into 100 equal-frequency groups. The range is a measure of dispersion, defined as the difference between the largest and smallest observed values (maximum minus minimum) — it is anchored on the data's extremes, not on zero.
Application
Evaluate each statement against these definitions:
Statement I says a percentile divides the distribution into 100 equal parts. This matches the standard definition of percentiles (P1 to P99 cut the ordered data into 100 equal-frequency segments). Statement I is TRUE.
Statement II says range is the distribution between zero and the highest value. Range = highest value minus lowest value; the lower anchor is the smallest observed value, which need not be zero (it can be negative or any minimum). Tying it to zero is wrong. Statement II is FALSE.
Cross-check / contrast
A quick counterexample fixes Statement II: for the data {12, 15, 20}, the range is 20 - 12 = 8, not 20 - 0 = 20. The minimum (12), not zero, is the lower bound. So exactly one statement holds: Statement I is true and Statement II is false.