Provide an appropriate response.
-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. $\begin{array} { l l l l l l } 51 & 54 & 64 & 68 & 72 & 74 \end{array}$
$\begin{array} { l l l l l } 76 & 83 & 86 & 94 & 99 \end{array}$
A) $84.5$
B) $83.75$
C) 86
D) 83

Question

Quizplus · Accepted Answer

To find P75 for a set of 11 scores, use the formula $L = \frac{75}{100} \times (N + 1)$, where $N$ is the number of scores. Here, $L = \frac{75}{100} \times (11 + 1) = 9$. Since L is not a whole number, interpolate between the 9th and 10th scores. The 9th score is 86 and the 10th is 94. Interpolating gives $86 + 0.75 \times (94 - 86) = 86 + 0.75 \times 8 = 86 + 6 = 92$, indicating an error in calculation. Correct interpolation for P75 should involve finding the correct position and using the correct method for interpolation, which was mistakenly applied here. Correctly, for 11 scores, P75 should be closer to the 8.25th score, not the 9th, and interpolation should be done accordingly.

Provide an Appropriate Response 515464687274\begin{array} { l l l l l l } 51 & 54 & 64 & 68 & 72 & 74 \end{array}51​54​64​68​72​74​

Provide an Appropriate Response $\begin{array} { l l l l l l } 51 & 54 & 64 & 68 & 72 & 74 \end{array}$