In statistics we have learnt about Quartiles, as the name suggests Quartiles are the values that which divide the given list into quarters. We have the first quartile which is the lower quartile, second quartile which is the median and the third quartile which is the upper quartile in a given list arranged in a numerical order. Let us now learn about percentiles or centiles, they are similar to quartiles but the difference is that Percentile divides the given list into hundred equal parts and the most important thing about centile is that it measures the position from the bottom. This is used when large set of data is used something like SAT scores or graduating standings and other test scores with large data.
Percentile is most commonly used to determine the relative standing of a student in a huge group or in other words the rank position of the student or individual. It is the easiest way which helps to tell where the individual stands at graduation when compared to other graduates that is at what centile. We can define centile as a measure used to determine what percent of the total frequency scored below that particular measure. For calculating percentile we need a formula, to deduce the formula, let us assume the centile rank of a score to be some, x, out of a total score of n, excluding x, then we can calculate percentile using the formula; we first divide (number of scores that are below x) by n and then multiply the quotient with 100, the final value we get gives us the centile rank for that particular score. Let us consider an example for better understanding of the usage of the above formula. Let us assume that Edison graduated 15th out of a class of 200 students, which means there are 185 students who were ranked below Edison. Let us now calculate centile rank for Edison’s score, here x = 15 which means the number of scores below x = 200 – 15 = 185 as total students= n = 200.
(Number of scores below x)/n. (100) = (185/200).(100) = 92.5 = 93rd centile on rounding
The centile shows that Edison stands at the 93rd centile in the class which is higher than 93% of the graduates.
Percentile Chart
The information given below in the centile chart refers to the scores on a standardized test.
Test Score Centile
800 92
700 88
600 79
550 50
400 45
350 38
300 25
From the above centile chart we can determine the percent of test takers according to the scores mentioned. For example let us find the percent of test takers who have scored greater than or equal to 700, from the chart it is clear that 88 % of the test takers have scores less than 700 which means the rest of them have scored greater than or equal to 700, so we get, 100 – 88 = 12% of the test takers who have scored greater than or equal to 700.
Percentile is most commonly used to determine the relative standing of a student in a huge group or in other words the rank position of the student or individual. It is the easiest way which helps to tell where the individual stands at graduation when compared to other graduates that is at what centile. We can define centile as a measure used to determine what percent of the total frequency scored below that particular measure. For calculating percentile we need a formula, to deduce the formula, let us assume the centile rank of a score to be some, x, out of a total score of n, excluding x, then we can calculate percentile using the formula; we first divide (number of scores that are below x) by n and then multiply the quotient with 100, the final value we get gives us the centile rank for that particular score. Let us consider an example for better understanding of the usage of the above formula. Let us assume that Edison graduated 15th out of a class of 200 students, which means there are 185 students who were ranked below Edison. Let us now calculate centile rank for Edison’s score, here x = 15 which means the number of scores below x = 200 – 15 = 185 as total students= n = 200.
(Number of scores below x)/n. (100) = (185/200).(100) = 92.5 = 93rd centile on rounding
The centile shows that Edison stands at the 93rd centile in the class which is higher than 93% of the graduates.
Percentile Chart
The information given below in the centile chart refers to the scores on a standardized test.
Test Score Centile
800 92
700 88
600 79
550 50
400 45
350 38
300 25
From the above centile chart we can determine the percent of test takers according to the scores mentioned. For example let us find the percent of test takers who have scored greater than or equal to 700, from the chart it is clear that 88 % of the test takers have scores less than 700 which means the rest of them have scored greater than or equal to 700, so we get, 100 – 88 = 12% of the test takers who have scored greater than or equal to 700.
