Percentiles compare a student’s performance to that of others who took the same test, with a number between 1 and 100 indicating their ranking. They are calculated by sorting values in ascending order, finding the numerical position of a result, subtracting 0.5, dividing by the number of results, and multiplying by 100. Percentiles are widely used in education to assess individual and comparative performance, identify areas for improvement, and control tests in population groups. They also have applications in scientific analysis, social and opinion polls.
A percentile is best described as a comparison score. The concept is used extensively in statistical analysis, but many will be more familiar with the term as it relates to standardized testing in schools. Unlike a percentage, in which a student is assigned a percentage number that correlates only with how well they performed on a test or exam, a percentile is a number between 1 and 100 that relates the student’s performance to that of other students who took the test. In a set of numbers, the percentile for a given value indicates the percentage of numbers that are less than or equal to that value. For example, if a student scores 85% on a test and is in the 90th percentile, that means 90% of the students scored less than or equal to 85%.
The concept may be easier to understand by comparing it to percentage scores. A simple example might be a test with 100 problems, each worth 1% of the test. If a student answers 80 problems correctly, she gets an 80% score. In some cases, performance can be ranked on ranges, for example an “A” grade might indicate 90% or higher, a “B” grade might indicate 80-89%, and so on. These grades may be based on the number of students who would normally fall into each category, but by themselves they are not a comparison to other students. If this student’s performance on the test is in the 95th percentile, then 95% of those who took the test scored at or below 80% or, to put it another way, are in the top 5%. .
Calculation of percentiles
To calculate percentiles for a result set, the values are first sorted in ascending order. The percentile for a given value can then be found by subtracting 0.5 from its numerical position in the sequence, dividing by the number of results, then multiplying by 100. For example, if there are 25 results with values between 31 and 93 and the result 47 is the tenth in numerical order, the percentile for this result is 10 – 0.5, divided by 25, then multiplied by 100, yielding 38. This means that 38% of the results are less than or equal to 47. It is also possible to do the calculation for hypothetical outcomes that did not actually occur, i.e. find what the percentile would be for that outcome.
Percentiles in education
While this statistical method has many applications, one of the best known is in education. Especially when the test is standardized, it is meant to serve a diverse group of people and accurately measure not only individual performance, but comparative performance as well. When looking at a data set, percentiles can help you better assess the average or average student achievement. Many students will cluster in the middle area, earning percentiles anywhere from 25 to 75, while some will far exceed it, reaching the 90s range. The mean and median scores are calculated into the expected results and can show how well most people are performing and how well any individual student is performing.
Percentiles can further show if you are performing poorly in certain areas. If every student taking a test answers the same question incorrectly, or if most average students do, this could indicate a problem. It may be that the question is poorly worded or that this area of the subject was not adequately covered in the course. With tests becoming more standardized in academia, this method can eliminate wrong questions and identify areas for improvement in courses or teaching methods.
Another educational use of percentiles is to control tests in population groups. For example, an entire high school in an urban neighborhood may score well below average on academic tests. Even if a couple of pupils do well – these are known as outliers – it is clear that there is a problem. It is possible that children are not adequately prepared to take the test or that the test is not understood by students due to cultural or language barriers. By considering percentiles and percentage scores, schools can better address all of their students’ needs.
Other applications
Percentiles have many other applications and can be found in many studies that use statistics. In the scientific analysis of samples, this method can highlight important trends or problems. Scientists can, for example, test a series of air samples taken from an urban area for their sulfur dioxide content in parts per million (ppm). If the safe level is defined as 3ppm and the percentile for 3ppm is 35%, it can be said that 65% of the samples exceed the safe limit and action is needed to reduce pollution levels. Other uses include analyzing the results of social polls and opinion polls.
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