Which value of X is exceeded by 90% of the 20 recorded observations?
2011
Which value of X is exceeded by 90% of the 20 recorded observations?
Answer: C. 61 — ConceptFor a candidate threshold x, its exceedance percentage is (number of observations strictly greater than x / total number of observations) × 100.…
- A.
63
- B.
62
- C.
61
- D.
60
Show answer & explanation
Correct answer: C
Concept
For a candidate threshold x, its exceedance percentage is (number of observations strictly greater than x / total number of observations) × 100. Therefore, a value exceeded 90% of the time must have 18 of the 20 observations above it.
Application
Arrange the 20 observations in ascending order: 60, 61, 62, 62, 63, 63, 64, 64, 64, 64, 65, 65, 65, 66, 66, 66, 67, 68, 69, 70.
For x = 61, the observations greater than 61 run from 62 through 70, giving 18 observations.
Compute the exceedance percentage: (18 / 20) × 100 = 90%.
Cross-check
Only 60 and 61 are not greater than 61, so 20 − 2 = 18 observations exceed it. Hence, the required value of X is 61.