What is percentile rank of 20? Please answer correctly. The ACT math scores of 15 high-school seniors: 18 15 25 24 21 17 32 30 20 27 28 24 18 27 28

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2022-08-15

What is percentile rank of 20? Please answer correctly.
The ACT math scores of 15 high-school seniors:
18 15 25 24 21 17 32 30 20 27 28 24 18 27 28

Answer & Explanation

Hamza Conrad

Hamza Conrad

Beginner2022-08-16Added 20 answers

Percentile rank of a score indicates the percentage of data that is equal of less than the score. Quartiles divide the data into 4 equal parts.
Quartiles are based on percentiles. Percentile is a statistic measure, Xth percentile indicates that X% so the data falls below Xth percentile.
To calculate the percentile rank, first arrange the data in ascending order.
15,17,18,18,20,21,24,24,25,27,27,28,28,30,32
It can be seen that 4 numbers are less than 20, so 5 numbers are less than or equal to 20 out of 15 observations. So L=5, N=15. Thus the percentile rank of 20 is calculated below.
Percentile rank = L N × 100 = 5 15 × 100 33.33
Percentile ranks are expressed in whole numbers, so percentile rank of 20 is 33 (rounding 33.33). This indicates that approximately 33% of the data are less than or equal to 20.

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