When it comes to analyzing and comparing data, percentile rank can be a useful form of statistical analysis.
This is a calculation that not only offers you information and data, but which also places that data in context and relation to comparative statistics.
This can offer useful insights, and allow you to use data in a more effective manner, particularly in real-world scenarios.
What Is Percentile Rank?
In the simplest terms, percentile rank is a statistical measure that tells you where someone falls within a group or population. The percentile is the percentage of ranking items that appear either at a certain score or below a certain score.
For example, if you take a standardized test for school or work, and your result is scored at either equal to or greater than 90% of all other scores of those who have taken this test, your percentile rank will be in the 90th percentile.
Unlike a percentage score – which we will explore in greater detail later – percentile rank is not an indicator of how well you have done on a particular test or exam, but rather the rank that you hold as part of a larger group – in this case, your peers.
Calculating Percentile Rank
Percentile rank can be calculated using a simple equation:
Percentile rank = p/100 x (n+1)
Here, p is used to represent the percentile rank (so in the example above, 90%), and n is used to represent the total number of items that have been included in that particular data set – for example, the number of people who took the test. If we say that the data set was 1000, the equation in this example would be 90/100 x (1000 + 1).
To start, you will need to know the percentile of the item that you are ranking for this study – this could be the percentile of a student’s SAT score. The equation for this is:
Percentile = (number of values below score) / (total number of scores) x 100
As an example, say that a student’s raw score is 1280 out of 1600 on their exam, they can use the percentile formula to see where this places them compared to their peers. In order to determine the percentile rank, you will need to first work out the percentile of the specific score. There are a few steps to help you achieve this:
Put Data in Ascending Order
The first step is to place values in ascending order, from low to high. For example, say that you receive a data set of test scores of 67, 54, 99, 101, 121, and 89, you would first arrange these into ascending order – 54, 67, 89, 99, 101, and 121.
Divide the Number of Values By The Total
Next, you will need to determine how many of these values – the test scores – fall below the score that you are measuring percentile for. As an example, say that the student’s score is 89 – you would consider the data set above to determine how many scores there are that fall under this value – the answer is 3.
Now, count the total number of values in this set – 6. Once you have these figures, you can use the formula we discussed above:
Percentile = (number of values below score) / (total number of scores) x 100
Percentile = (3) / (6) x 100
Once you have a number from the equation, you can multiply this by 100 to provide you with a percentage. Our equation then becomes:
Percentile = (3) / (6) x 100 = 0.5 x 100 = 50%.
The score of 88 is therefore in the 50th percentile.
The higher your percentile rank, the better that you have performed in that particular study or activity compared to your peers – in the example above, the student is likely fairly average, as their performance and result placed them firmly in the middle of the overall results, or in the 50th percentile.
What Is Percentile Rank Used For?
Percentile rank is useful in a number of settings, and the most common tend to be educational and examination situations. Some key examples include:
Testing And Assessment
The percentile rank is often the chosen method of statistical analysis used in education, and this tends to be popular for analyzing test scores and student performance.
This form of analysis allows you to compare how your child or student performed compared to their peers – that is, students of a similar age and ability level – and can offer a clearer overall picture of where a child is struggling, and where support or additional assistance should be put in place.
This data can be particularly useful if you are seeking admission to a specific, specialized program, considering additional support or special education, or trying to ensure that a pupil is placed correctly.
Language Testing
Percentile ranks can also be useful when it comes to language tests, and this is particularly true for younger children.
Those of kindergarten age will have a wide range of verbal and language skills, and, on occasion, concerns and issues may arise about the child’s ability to speak and communicate with those around them.
In these situations, speech therapists and experts can use percentile ranks to ascertain the verbal abilities that each child has, and how this compares to their peers.
In order to establish an “average range” on these language tests, experts need to know the number of items that are answered correctly by children of different ages – as a general rule, younger children get fewer right answers than older children.
And most tests will be designed to allow children to continue to answer until they start missing questions – this demonstrates the very upper limits of their abilities. Percentile ranks can then be used to ascertain where a child is in comparison to their peers.
When using percentile rank scores for this purpose, it is important not to conflate percentile rank and percentage scores – these are very different figures. Percentage scores are calculated by taking the score that a student achieved on a particular piece of work and dividing this by the total number of marks available.
This score is then multiplied by one hundred to give a percentage. These scores are great for helping teachers and parents to determine how well a single, particular child performed on one test, but are not useful for placing this score in a wider context – for example, comparing this to their peers.
Final Thoughts
Percentile ranking is a very useful tool for statisticians and offers a chance to see a piece of data in a wider context. This application makes the method very popular for educators and examiners, and many standardized tests or specialist entrance exams will usually have a specific cut-off to allow entry to students.
As an example, a college may require an SAT score in the 80th percentile in order to gain entry to a course.
Knowing how to calculate this figure, therefore, is an important part of building a strong, steady revision or study plan, as well as giving you an indication of your chances of success.
Though it may seem a little complex at the start, the basic equations are clear and direct once you have had a little practice, and this is a great addition to add to your mathematical and statistical toolkit.
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