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Percentile
Shikha Pandey
What is percentile?
“Percentile” is in everyday use, but there is no universal definition for it. The most common definition of a percentile is a number where a certain percentage of scores fall below that number. You might know that you scored 67 out of 90 on a test. But that figure has no real meaning unless you know what percentile you fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test. Percentiles are commonly used to report scores in tests, like the SAT, GRE and LSAT. For example, the 70th percentile on the 2013 GRE was 156. That means if you scored 156 on the exam, your score was better than 70 per cent of test takers. A percentile may be denied as a point on the score scale below which a given per-cent of the cases lie. Percentile facts: The 25th percentile is also called the first quartile. The 50th percentile is generally the median The 75th percentile is also called the third quartile. The difference between the third and first quartiles is the interquartile range.
Calculation of the percentile
The formula for computation of percentile is as follows: Percentile, P= L +
[(^
pN
− F
]
f ×i Where L= Lower limit of the percentile class N= total of all the frequencies F=total of the frequencies before the percentile class f= Frequency of the percentile class i=size of the class interval p= No. of the percentile which has to be computed
Below is a problem based on this formula.
Example problem 1
Scores f 70-79 3 60-69 2 50-59 2 40-49 3 30-39 5 20-29 4 10-19 3 0-9 2 N= Calculate the 25th^ percentile. Here,
P 25 =
[(^
25 × 24
]
× 10
P 25 = 19.5 +
× 10
P 25 = 19.5 + 2.
P 25 = 22
What is percentile rank?
The word “percentile” is used informally in the above definition. In common use, the percentile usually indicates that a certain percentage falls below that percentile. For example, if you score in the 25th percentile, then 25% of test takers are below your score. The “25” is called the percentile rank. In statistics, it can get a little more complicated as there are actually three definitions of “percentile.” Here are the first two (see below for definition 3), based on an arbitrary “25th percentile”: Definition 1: The nth percentile is the lowest score that is greater than a certain percentage (“n”) of the scores. In this example, our n is 25, so we’re looking for the lowest score that is greater than 25%.
R 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 S 44 42 40 37 36 35 32 29 28 25 22 21 20 17 15 13 12 10 9 8 Clearly, the 14th^ rank has the score of 17, R= 14 and N= 20 Thus, Percentile ranking, PR =^100 −
100 R − 50
N
= 100 – 100x14 –
= 100 – 1400 –
=100 –
=100 – 67. =32.
Grouped data
For the computation of grouped data the formula is as follows: Percentile rank, PR =^
N [
F +(
X − L
i )
f
]
Where N= Total number of cases in the given frequency distribution F= Cumulative frequency below the interval containing score X X= Score for which we want to percentile rank L= Actual lower limit of the interval containing X i= Size of the class interval f= Frequency of interval containing X
Example problem 3
Calculate the percentile rank
Computing the cumulative frequency first, Here, F = 5 X = 22 L = 19. i = 10 f = 4 N = 24
