When finding percentiles, if the locator L is not a whole number, one procedure is to interpolate so that a locator of 23.75, for example, leads to a value that is 3/4 of the way
Between the 23rd and 24th scores. Use this method of interpolation to find P75 for the set of
Test scores below. $$\begin{array} { l l l l l l }
51 & 54 & 64 & 68 & 72 & 74
\end{array}$$
$\begin{array} { l l l l l } 76 & 83 & 94 & 94 & 99 \end{array}$
A)83
B)88.5
C)85.75
D)94

Question

When finding percentiles, if the locator L is not a whole number, one procedure is to interpolate so that a locator of 23.75, for example, leads to a value that is 3/4 of the way
Between the 23rd and 24th scores. Use this method of interpolation to find P75 for the set of
Test scores below. $$\begin{array} { l l l l l l } 
51 & 54 & 64 & 68 & 72 & 74
\end{array}$$
$\begin{array} { l l l l l } 76 & 83 & 94 & 94 & 99 \end{array}$
A)83
B)88.5
C)85.75
D)94

Quizplus · Accepted Answer

To find P75 (the 75th percentile) for the given set of 11 scores, we first calculate the locator $L$. Since there are 11 scores, $L = \frac{75}{100} \times (11 + 1) = 9$. This means we need to find a value 3/4 of the way between the 9th and 10th scores. The 9th and 10th scores are 94 and 94, respectively. Interpolating 3/4 of the way between two identical scores still results in the same score, so P75 is 94. However, given the options and the context of interpolation, it seems there might have been a misunderstanding in the calculation or interpretation of the question. Normally, if L is not a whole number, you would interpolate between the two closest ranks. But in this case, with the scores provided and the typical method of finding percentiles, the correct answer based on the usual interpretation of percentile calculation would directly be the value at the locator's position if the scores were different. Given the misunderstanding and the options provided, the correct interpretation based on the expected process of interpolation (and assuming a need to interpolate between different values) would not directly apply to the provided scores as they lead directly to a score of 94 without the need for interpolation. This indicates a discrepancy in the understanding or the provided options.

When Finding Percentiles, If the Locator L Is Not a Whole