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Which expression gives the percentile of a particular value, where x counts values below it and y counts values equal to it?
A(x + 0.5y)/n times 100
B(x + 2y)/n times 100
C(x - 0.5y)/n times 100
D(0.5x + y)/n times 100
Answer & Solution
Correct answer: A. (x + 0.5y)/n times 100
1. The count x holds every value below the one of interest.
2. The tied values are counted by y, and half of them are credited to the value itself.
3. The total x plus half of y is divided by n and multiplied by 100, then rounded to the nearest whole number.
4. Subtracting half of y would discount the ties instead of splitting them, so that version understates the percentile.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.2 Measures of the Location of the Data_
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