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Percentile

Apercentileis a comparison score between a particular score and the scores of the rest of a group. It shows the percentage of scores that a particular score surpassed. For example, if you score 75 points on a test, and are ranked in the 85 thpercentile, it means that the score 75 is higher than 85 % of the scores.

The percentile rank is calculated using the formula

R = P 100 ( N )

where P is the desired percentile and N is the number of data points.

Example 1:

If the scores of a set of students in a math test are 20 , 30 , 15 and 75 what is the percentile rank of the score 30 ?

Arrange the numbers in ascending order and give the rank ranging from 1 to the lowest to 4 to the highest.

Number 15 20 30 75 Rank 1 2 3 4

Use the formula:

3 = P 100 ( 4 ) 3 = P 25 75 = P

Therefore, the score 30 has the 75 thpercentile.

Note that, if the percentile rank R is an integer, the P thpercentile would be the score with rank R when the data points are arranged in ascending order.

If R is not an integer, then the P thpercentile is calculated as shown.

Let I be the integer part and be the decimal part of D of R . Calculate the scores with the ranks I and I + 1 . Multiply the difference of the scores by the decimal part of R . The P thpercentile is the sum of the product and the score with the rank I .

Example 2:

确定 35 thpercentile of the scores 7 , 3 , 12 , 15 , 14 , 4 and 20 .

Arrange the numbers in ascending order and give the rank ranging from 1 to the lowest to 7 to the highest.

Number 3 4 7 12 14 15 20 Rank 1 2 3 4 5 6 7

Use the formula:

R = 35 100 ( 7 ) = 2.45

The integer part of R is 2 , calculate the score corresponding to the ranks 2 and 3 . They are 4 and 7 . The product of the difference and the decimal part is 0.45 ( 7 4 ) = 1.35 .

Therefore, the 35 thpercentile is 2 + 1.35 = 3.35 .