Percentage and Percentile are similar concepts but have some differences between them. Percentage is used to express the mathematical calculation in terms of per 100, whereas percentile is used to express the relative value with respect to other data present.
In other words, Percentage is a ratio between a part and whole per 100 while Percentile is a representation of data in comparison with other data present in the dataset. Both Percentage and Percentile are related concepts but very different from each other, as they are used to represent data in two completely different ways.
In this article, we will understand both Percentage and Percentile in detail, understanding their difference in the expression of data.
What is Percentage and Percentile?
The word “Percent” is derived from the Latin word “Per Centum”, meaning “by hundred”. Percentage is a proportion or ratio of a part and whole which is represented by a value with a condition that the whole will always be 100. It is represented by the % sign which is read as percent or “for every 100 parts” of any particular group of data. In other words, Percent means per hundred.
Meanwhile, Percentile is a type of mathematical quantity that determines the performance of a particular data (x) in comparison to other data in the dataset. It helps us understand the frequency distribution of data. We can calculate the order of data using percentile or vice-versa, in other words, to find percentile we always need to sort the data. It is very important to have data in order to calculate the value of percentile or centile.
Definition of Percentage
Percentage is a fraction in which the value of the whole(denominator) is 100. It is represented in the form of a fraction or ratio with a % sign. Examples of Percentages, where we can see the different forms of representation of percent.
- 45% = 45/100 = 0.45
- 10% = 10/100 = 0.1
- 90% = 90/100 = 0.9
Definition of Percentile
Percentile or a centile is a mathematical measure used in the field of statistical calculations which defines how a particular data, person, item or group compares to others in dataset. It also indicates the percentage of scores that fall below a particular value, showing where the value compares relative to other values in a group.
Example of Percentage and Percentile
If a student named Isha, scores 89 marks her science exam out of a total score of 100, she has scored 89% aggregate in her exam. In other words, Isha has scored 89% in her science exam. We can see examples of percentage in every sector of life, from description of distribution of population across the world to everyday exams, Whenever Numbers, Calculations and representation of numbers visually is concerned, Percentage come into picture.
Meanwhile In Percentile, we have to sort and compare Isha Science score with the score of total 30 students in Class 6th. We will first sort the science exam score of 30 students. For example, if the score is 89th Percentile, it would mean that her score is better than 89% of students. Percentile is important to understand and spot the trends and distribution of data.
Significance of Percentage and Percentile
Percentage is per 100 count. For example, you planted 100 trees, but 10 of the trees did not grow well. To represent this scenario, we may also express 90% of the trees flourished well. But this was countable small numbers, but what if the numbers represent the population of a country, a state or even world. Percentage makes things visually representative and easier to understand, according to needs.
- Percentage is used to compare various quantities of an object. For example, Number of students present in Class 5th in a school is 30 % greater than the number of students present in Class 6th.
- Percentage can also be used to compare quantities of two different objects.
- We can also calculate ratio and proportion using Percentage.
Percentile, on the other hand is the comparison from others present in the group. For example, you scored 4th rank in your math test in your class which consists of 40 people. In this case, you scored less than 3 students (First, second and third rank students) but more than 36 students in your class, in this example, your score would be around 90 percentiles approximately. Percentile is important measurement tool in statistics which describes,
- Comparision with remaining dataset, to evaluate performance among peers. This helps to identify outliers.
- Risk Assessment in finance and investment to evaluate and calculate the returns, percentiles play a major role in identifying those data which are performing exceptionally well.
How to Calculate Percentile?
To calculate Percentile any score x, we can divide “number of values below x” and total count of data in dataset which is then multiplied by 100. Please note that the data in dataset should be sorted.
Percentile (x) = (Number of values that fall below “x” / total number of values) ×100
How to Calculate Percentage
Calculation of Percentage is used in everyday needs, and it uses a simple formula Percentage = (X/Y) × 100. We can also describe this formula as parts (of any whole) divided by Whole and then multiply it by 100.
Percentage (%) Formula = Parts/Whole × 100
Difference Between Percentage and Percentile
Both Percentage and Percentile are used to calculate measurements, still there is fine difference between both of them. Lets look into these differences one by one to understand each term better.
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Percentage is a way to express part of a whole as a fraction of 100 to represent the comparison in the form of ratio or proportion.
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Percentile is statistical measure that express the relative position of a particular value in the whole database.
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Percentage calculation doesn’t necessarily require sorting data.
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Percentiles are calculated based on sorting data. Data should be sorted in order to find Percentile.
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The Place value of a data (the rank order of number) in dataset has no influence on percentage calculations.
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The place value of a data (where a value stands in dataset) heavily influences the percentile calculations.
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It is used to represent proportions in everyday life.
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it is used to represent relative proportion of a value within dataset.
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For example, scoring 80% in a test would mean you got 80 out of 100 questions correct.
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For example, scoring 80th percentile would mean you got better than 80% of students who attended the test.
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It is used for Simple Comparisions.
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It is used for detailed information, useful for comparing data frequency distributions.
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Percentage is very common and popular for simple calculations and easy quantifiable measure.
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Percentile is not very common in everyday life as it requires complex calculations and sorting.
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Overall Percentage and Percentile, they both have different calculation methods and applications, where percentage is a simple and direct calculation method useful for measuring per 100, Percentile is a relative position of a value in any dataset. To understand these mathematical aspects, check out these solved examples, which will help you get an understanding of the mathematical formula of the terms.
Also, Check
Solved Examples on Percentage and Percentile
Example 1. Find 20% of 1500?
We can find percentage by using, Percentage (P) = parts(x1)/whole(x)
P = x1/x
⇒ 20% = x1/1500
⇒ x1 = 20✕1500 /100 = 300
So, 20% of 1500 is 300.
Example 2. If Ram score 78 marks out of 100, how much percentage he scored?
Ram scored 78/100 × 100 = 78%
Example 3. What is 50% of 10?
To solve this, we will use percentage trick.
% x of y = %y of x
⇒ 50% of 10 = 10% of 50
On solving this, we will get 5 as answer.
Example 4. Find percentile for the value 16 from the given population 11, 16, 17, 13, 18, 19.
First we will sort data in ascending order. Sorted Data : 11,13,16,17,18,19
Number of values that fall under 16 = 2
Total count of values = 6
Percentile = Number of values that fall under 16 / Total count of values ✕ 100
⇒ Percentile = 2 / 6✕ 100 = 33.33
Hence, The percentile of value 16 for the given population is 33.33
Example 5. What is the 5th percentile for the given population of weights of persons 5, 5, 4, 6, 10, 9, 9, 6, 8, 7.
The given data is not sorted. So first sort the data in ascending order. After Sorting the data is arranged in this order : 4,5,5,6,6,7,8,9,9,10
Given, Percentile (P)= 5
Total count of values = 10
We Need to find the 5th percentile for the given data. Lets call it A.
Percentile = (A /Total Count) x 100
From the given formula we can find A by
A= (P x Total count)/100
⇒ A = (5 x 10) / 100
⇒ A = 50/100
⇒ A =1/2
0.5 can be rounded off to 1
And 1st term in the sorted population is 4. 5th percentile value is 4.
Example 6. Isha was trying to get percentage of red balls, when she had 12 blue balls, 8red balls, and 5yellow balls. Help her out in calculating the percentage of red balls?
Total balls = red balls + blue balls + yellow balls = 8 + 12 + 5 = 25
Red balls = 8
Percentage of red balls = Number of Red Balls / Total Balls × 100
⇒ Percentage of red balls = (8✕4/25✕4) ×100 = 32/100 = 32 %
Isha has 32% red balls.
Practice Problems on Percentage and Percentile
Q1. If you have 13 red balls, 7 yellow balls, 12 blue balls. Calculate the individual percentage of each red, yellow and blue balls.
Q2. Find 37 % of 1500.
Q3. Find 45% of 13200.
Q4. Find 400 % of 128.
Q5. Find percentile for the value 16 from the given population 11, 16, 17, 13, 18, 19.
Q6. Find percentile for the value 16 from the given population 11, 16, 17, 13, 18, 19.
Q7. What is the 35th percentile for the given population of weights of persons 65, 56, 64, 66, 160, 69, 96, 65, 85, 70.
Q8. What is the 8th percentile for the given population of weights of persons 50, 95, 14, 16, 10, 19, 19, 17.
Percentage and Percentile – FAQs
1. What is Percentage?
Percentage is a number that represents the fractional part of percent.
2. What is Percentile?
Percentile is a number below which a certain percent of number in the form of data falls.
3. What is the difference between Percentage and Percentile?
Percentage is used to represent value per 100 while Percentile is used to represent which rank data stands in the dataset.
4. What is the difference between interpretation of Percentage and Percentile?
If Isha scores 85% in exam, it will be interpreted as she solved 85 out of 100 questions correctly.
If Isha scores 85th percentile, it will be interpreted as she performed better than 85% of students who appeared in the exam.
5. Can Percentage be greater than 100?
Yes, Percent can be greater than 100.
6. Why is Percentile Important?
Percentile is important to recognize pattern, understand performance and distribution frequency.
7. Is Percentage and Percentile same? List any one of the situations.
No, Percentage and Percentile are not same. They cannot be same in any situation as there interpretation and method of calculations are different.
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