Introduction
We surely have come across the words percentage, and percentile a lot. Both percentage and percentile are widely used mathematical terms that provide a value using a given data. They are different in terms of their concept and usage. However, many of us do not have a clear picture of the differences between the two.
Percentage is a measurement used to find a value in terms of 100. Percentile, however, measures the rank or position of something or someone compared to others. Percentile uses distributive data, whereas percentage does not. A percentage gives us a value after comparing a score with the total score. It means that the percentage only focuses on individual performance. Percentile, contrastingly, compares individual performance with others involved in the same group. For example – Comparing a student's performance by ranking his performance among the other students. Hence, both of them are required for different purposes.
Let us look into further differences between a percentage and a percentile through this article.
Percentage vs Percentile
Many mistaken percentages and percentiles to be the same. That may be because most of us are unaware of what a percentile is, and both percentage and percentile sound similar. Percentage and percentile are two different mathematical concepts that have varied usages.
A percentage provides us with the individual score or value out of 100, while a percentile shows us where a case stands compared to other cases. A percentage can be written in the form of ratios and decimals, whereas we cannot say the same for a percentile. Percentages express individual performances, whereas percentiles express relative performances.
Likewise, several other points make the percentage and percentile different from each other.
Differences Between Percentage and Percentile in Tabular Form
| Parameter | Percentage | Percentile |
| Definition | It is a mathematical unit that provides a value out of 100. | It is a mathematical term that describes how a score compares with other values from the same set. |
| Unit | Its unit is denoted by %, for example, 70% | Its unit is denoted by xth, for example, 50th |
| Ratio form | We can also express a percentage in the form of a ratio. | A percentile cannot be expressed in the form of a ratio. |
| Decimal form | It can also be written in the form of a decimal. | It cannot be written in a decimal form. |
| Rank of numbers | A percentage does not find the rank of numbers. | We use a percentile to find the rank of numbers. |
| Cases | It is based on only one case. | It is based on comparing one case with several other cases. |
| Distribution | A percentage does not rely on a normal distribution. | A percentile relies on a normal distribution. |
| Objective | To show fractional or decimal numbers as whole numbers. | To show where the value stands in comparison with other values. |
What is a Percentage?
A percentage is a mathematical unit that measures the value of a number or scores out of 100. It is a fraction where 100 is taken as the denominator. The percentage is a relation between a 'part' and a 'whole' where the value of 'whole' always has to be 100. The term percentage is represented by the symbol '%' which is also called percent. The word percent is derived from the Latin and French origin words "per" and "cent" which translates to "per hundred".
A percentage can also be written in the form of a ratio like 50:100, or a decimal number like 0.5.
For example – Seema scored 60 out of 100 on her Math paper. The percentage of her Math subject would be 60/100×100, which is 60%.
If the same percentage has to be expressed in a decimal format then it can be calculated without multiplying 100 to the fraction like, 60/100 is 0.6.
Sometimes a score is made out of a different number than 100. It could be 30 out of 50. In this case, the percentage is calculated in this way - 30/50×100, the answer of which would be 60%.
Uses of Percentage
The percentage has many uses in our lives. From calculating discounts for a product to calculating the performances of students in their exams, we use a percentage for almost anything that includes numerals.
Some of the uses of a percentage are given below:
Used To Find Out "How Much" Or "How Many"
Percentage helps calculate the exact amount one is talking about.
For example – Let us assume Shreya earns 30,000 a month. She saves 30% of her salary every month. Therefore, the amount of money saved by Shreya = 30% of 30,000 = 30/100×30,000 = Rs 9,000.
Used To Compare Fractions
Percentage is required to compare one fraction to another. While it is clear which fraction is of higher value when the denominator is the same, it is difficult to compare the fractions when the denominators are different. That is when percentage comes in handy. We can convert fractions into percentages to get a clearer picture of the comparison.
For example – Jerry drank 4/6th of apple juice, and Sid drank 5/8th of the same. If we have to find out who drank more apple juice, we must convert the fractions into percentages and then compare the two. We can do that by the fractions by 100 which are shown below.
- Jerry drank 4/6×100 = 66.6% of the juice.
- Sid drank 5/8×100 = 62.5% of the apple juice.
Therefore, it becomes clear that Jerry drank more apple juice than Sid.
To Find The Percentage Increase Or Decrease
We often need to measure our progress in the workplace or in academics. We also need to calculate the financial aspects of our lives. The percentage can help in these matters as well.
For example – David was recently informed that his salary will be hiked by 6%. His salary before the hike was Rs. 25,000. To find out the amount of salary that will be added and the total amount he will receive after the salary hike, firstly, we need to calculate what 6% of 25,000 would be and then add it to the salary.
- 6% of 25,000 = 6/100×25000 = 1,500
Therefore, hiked amount is 1,500
- Salary after the hike = 25,000 + 1,500 = 26,500.
Therefore, we can use percentages to calculate an increment in salary or progress in academics.
How to Calculate Percentage?
The formula to find a percentage is:
[(Value given)/(Total value)] × 100
For example –
Q. Ritvik scored 480 out of 600 in his mind-year exams. What is his percentage?
Solution: To find his percentage we use the formula [(Value given)/(Total value)] × 100
We know that the value given = is 480 and the total value = 600. Therefore, the percentage would be 480/600 × 100 = 80%. Therefore, Ritvik's percentage is 80%.
What is Percentile?
Percentile is a new term for many individuals. We do not use it as often as percentages. Only those who have appeared for competitive exams must have come across the term in most cases.
Percentile is a measurement in statistics that provides the percentage of values that are under a specific value. It shows how much above a score is from a certain percentage of scores. It is a comparison of a score with other scores. Since it compares a given value with the rest of the data, it needs to take note of all the data of a particular group. A percentile cannot be calculated only with an individual score.
For example – Charlie got 95th percentile in a competitive exam. That means that Charlie scored more than 95% of the candidate and scored less than 5% of the candidates.
Thus, a percentile reflects how well one has performed compared with others.
Percentiles can also refer to quartiles. Quartiles are a type of percentiles that are classified into the following:
- The first quartile also referred to as Q1, is the lowest quartile. It corresponds to the 25th percentile. It means that the value of 25% fall under the first quartile.
- The second quartile, or Q2 is the median quartile that corresponds to the 50th percentile. It means that 50% of the data falls under the second quartile.
- The third quartile, or Q3 is the upper quartile. It includes the 75th percentile, which means that 75% of the data falls under the third quartile.
Percentiles are split into 25th, 50th, and 75th percentiles to divide the data into four equal parts. The data are divided equally into four groups.
Uses of Percentile
Percentile is used in figuring out where a value stands compared to the rest of the values. Here are some of the uses of percentile:
To Compare Our Performance
Percentile is very helpful for us to understand how well we did in a test compared to others.
For example – If Rohan's percentile is 86th on a test, then he scored better than 86% of the students in his class.
To Compare Children's Growth
Percentile is used when we need to compare a child's height or weight or all-around growth with other children of the same age in an area or a classroom.
For example – Smita's weight of 40 kg is at the 56th percentile of weight for girls in the 7th standard. This means that Smita weighs more than 56% of the girls in her class.
Therefore, a percentile could indicate whether the weight of a child is healthy for its age or not. It can work the same way with the heights of children as well.
How to Calculate Percentile?
Percentile provides us a value that helps us in comparing a score with other given data. Percentile comes in handy in terms of comparing one's performance with others. The formula used to find out the percentile is = [(Number of values below x) ÷ (Total number of values)] × 100
For example –
Q. Anshu got the 7th position in the class in her half-yearly exams. His class has a total of 50 students. What is Anshu's percentile?
Solution: We know that Anshu got the 7th position. We also know that total number of students is 50. Therefore, students who scored less than Anshu = 50-7 = 43.
To know what Anshu's percentile is we have to follow the formula which is = [(Number of values below x) ÷ (Total number of values)] × 100 = 43 ÷ 50 × 100 = 86
Therefore, Percentile scored by Anshu = 86th Percentile.
Main Differences Between Percentage and Percentile in Points
- A percentage shows us the score in terms of 100. Percentile, on the other hand, presents a value compared to other data.
- A percentage can only present an individual score, however, a percentile declares the ranking of a score amongst other scores.
- A percentage is required to check improvements or downfall in our performance compared to past performances. However, the percentile is used to compare an individual's performance relative to others' performances.
- A percentage can also be written in the forms of fractions and ratios, whereas a percentile cannot be written in those forms.
- We can use a percentage to show the rate, whereas a percentile is used to show the rank.
- A percentage cannot be used to compare different scores, while a percentile is especially used to compare given values with the other data.
- The percentage does not refer to quartiles, whereas percentiles refer to quartiles.
- A percentage compares between actual score and the total score. In contrast, a percentile compares an individual score and the total number of students or candidates in an examination.
Conclusion
A percentage and a percentile are very important mathematical concepts that are often used to find the required information using numbers. We often tend to get confused between the two as they sound similar. However, both of them are different in terms of their usage.
While we mostly use a percentage to express a value out of 100, we use a percentile to show the position or ranking of a score compared to other data.
A percentage and a percentile use different formulas to find the required values. Both of them have their unique purposes.
Therefore, we can conclude that a percentage and a percentile are two different arithmetical units. We cannot compare which is more important than the other because both of them have different purposes and usages.
References
- https://www.cuemath.com/commercial-math/difference-between-percentage-and-percentile/
- https://www.scribbr.com/statistics/quartiles-quantiles/#:~:text=Quartiles%20are%20a%20type%20of%20percentile.,falls%20below%20the%20second%20quartile.
