Official ExplanationThe Rth percentile is a value at or below which lie R% of the data values. To find the Rth percentile for a data set, first put the data in order. Next compute k, using the formula \(k = n (\frac{R}{100})\), where n is the number of data values. If k is an integer, the Rth percentile is the average of the kth and
(k + 1)th data values. If k is
not an integer, round k up to the next greatest integer, say 1, and then the Rth percentile is the Ith data value. Tip: Do not confuse percentiles with percents .
A percentile is a value that acts as cut point for a specified percent. For the data presented in Quantity A, the value of k for the 90th percentile is \(k = n (\frac{R}{100})= 10 (\frac{90}{100})=9\). Thus, the 90th percentile is halfway between the ninth and tenth values. Hence, Quantity A is \(\frac{100+1400}{2 }= \frac{1500}{2}= 750\). The two quantities are equal.
Tip:In some other publications and online materials, a slightly different definition of percentile from the one given in this answer explanation is given. In those publications/online materials, the Rth percentile is a value below which lie R% of the data values. For continuous distributions (such as the normal curve), the two definitions are equivalent. For the GRE, just think of the Rth percentile as a value that splits the data into two parts so that R% is at or below that value and (100 — R)% is at or above it.
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