The value of X that is exceeded during 50% of the measurement period is:
2011
The value of X that is exceeded during 50% of the measurement period is:
Answer: C. 64 — ConceptFor a threshold x, its exceedance percentage is the fraction of observations strictly greater than x. To find the value exceeded 50% of the time, order…
- A.
66
- B.
65
- C.
64
- D.
63
Show answer & explanation
Correct answer: C
Concept
For a threshold x, its exceedance percentage is the fraction of observations strictly greater than x.
To find the value exceeded 50% of the time, order or count the observations and identify the candidate with exactly half of the observations above it.
Application
There are 20 observations, so 50% corresponds to 0.50 × 20 = 10 observations.
In ascending order, the values are: 60, 61, 62, 62, 63, 63, 64, 64, 64, 64, 65, 65, 65, 66, 66, 66, 67, 68, 69, 70.
The values strictly greater than 64 are 65, 65, 65, 66, 66, 66, 67, 68, 69, and 70—a total of 10.
Thus, 64 is exceeded by 10/20 = 50% of the observations.
Cross-check
For a threshold of 66, 4 observations are greater (20%).
For a threshold of 65, 7 observations are greater (35%).
For a threshold of 64, 10 observations are greater (50%).
For a threshold of 63, 14 observations are greater (70%).
Therefore, the required value is X = 64.