The test scores of 40 students are listed below. Find P56. $$\begin{array} { l l l l l l l l l l }
30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \
59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \
72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \
81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98
\end{array}$$
A) 73.5
B) 73
C) 74
D) 22.4

Question

The test scores of 40 students are listed below. Find P56. $$\begin{array} { l l l l l l l l l l } 
30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \
59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \
72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \
81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98
\end{array}$$
A) 73.5
B) 73
C) 74
D) 22.4

Quizplus · Accepted Answer

P56 is the 56th percentile, which means 56% of the scores are below it and 44% are above it. To find the value at the 56th percentile, we need to arrange the scores in order from lowest to highest, which gives:

$$30, 35, 43, 44, 47, 48, 54, 55, \mathbf{56}, 57, 59, 62, 63, 65, 66, 68, 69, 69, 71, 72, 72, 73, 74, 76, 77, 77, 78, 79, 80, 81, 81, 82, 83, 85, 89, 92, 93, 94, 97, 98$$

There are 40 scores in total, so the 56th percentile corresponds to the score that is $$\frac{56}{100} \times 40 = 22.4$$ positions from the bottom (recall that percentiles can have decimal values). Counting up from the bottom, we see that the 22nd and 23rd scores are both 73, so the 56th percentile score is also \boxed{74}.

The Test Scores of 40 Students Are Listed Below A) 735 B) 73 C) 74 D) 22

The Test Scores of 40 Students Are Listed Below A) 735
B) 73
C) 74
D) 22