Percentage and Percentile

A percentage is a mathematical value that expresses a number as a fraction of 100, represented by the symbol "%". It can be written as a fraction or decimal, and is commonly used to compare quantities by showing their ratios and proportions. This standard form helps in understanding relative sizes and making comparisons easier.

For example, if a student scored 65 out of 100 in a test, his percentage is:

\(Percentage = \frac{65}{100} \times100 =65\%\)

A percentile represents the percentage of values in a data set that fall below a given value. It is often used in ranking systems and reflects the position of a value within a distribution. Percentiles are denoted as "\(P^{th}\)," where 'P' indicates the specific percentile rank.

For example, imagine 100 students took a test. If 80 students scored less than you, your percentile is 80.

The difference between percentage and percentile can be best understood by a tabular comparison of the two, as given below:
 

The ratio of the part by the whole in the fraction of 100 is the percentage. So, it is calculated by the formula,

\(\text{Percentage} = \frac{\text{part}}{\text{total}} × 100\)

For instance, if a student scores 540 marks out of 600. Find the percentage.

To find the percentage we use the formula, that is,

\(\text{Percentage} = \frac{\text{part}}{\text{total}} × 100\)

Here, \(\text{part} = 540\)

\(\text{Total} = 600\)

So, \(\text{percentage} = {{ ({540\over 600}) }}× 100 = 90\%\)

We can easily understand how percentage works by taking a look at this pie chart showing a company's employees working on remote mode, from their home and the number of people working in the office:

The way of comparing the given value by the whole is by percentile. It is calculated by using the formula,

\(\text{Percentile} = \left( \frac{\text{Number of values below } x}{\text{Total number of values}} \right) \times 100\)

For instance, in a class of 60 students, Tom’s rank is 10th. Calculate Tom’s percentile in the class.

The percentile is calculated by the equation, 
 

\(\text{Percentile} = \left( \frac{\text{Number of values below } x}{\text{Total number of values}} \right) \times 100\)
 

Here, \(x = {60} { \ – \ } {10} = 50\)
 

\(\text{Total number of values} = 60\)
 

So, \(\text{percentile}={{({50\over 60})}} × 100 = 83.33\)

So, Tom’s percentile in the class is 83rd.

Percentile can be understood easily with the help of the image given below:

Learning percentages and percentile helps students in exams, data analysis, and decision-making.  Now let’s check some tips and tricks to master in percentage and percentile.

• Understanding the basic concepts: Percentage means out of 100 and Percentile is the percentage of value below the required value. 
   
• When working on percentages try to do the mental math, that is \(100\%\) of a number is \(1, 75\%\) of a number is \({3 \over 4}\), \(50\%\) of a number is \({1 \over 2}\), and \(25\%\) of a number is \({1 \over 4}\). 
   
•  When doing data ordering to find percentiles, arrange the data in ascending order.
   
• Remember quick conversions like \(50\% = \frac{1}{2}, \ 25\% = \frac{1}{4}, \) and \(10\% = 0.1\). These make solving problems faster.
   
• When comparing or finding percentiles, think in terms of "out of 100". This helps you visualize results clearly and avoid confusion.
   
• Parents can help their kids understand the concept by drawing a ladder with 100 steps and painting 40 of them, representing 40% of the ladder painted. We can also place a toy on the 85th step, which is the 85th percentile. 
   
• Teachers can conduct classroom activities, such as giving a kid 10 balloons and popping 4 of them. Now ask the students what percentage of the balloons were popped. Also, ask them to arrange the balloons in order of their size. The lowest balloon has the 1st percentile, and the largest balloon has the 100th percentile.
   
• Parents can make cards that easily help children identify the difference between a percentile and a percentage. Make a card that says, “How much? - Percentage”, “Where am I? - Percentile”.
   
• Teachers can use the test scores of the students to teach the concept of “what is the difference between percentage and percentile?” When a student gets 75 out of 100 on a test, he/she has scored 75%. It also means that the student scored better than 75% of the students, which is the 75th percentile.

The percentage is used in our daily life in other fields such as finance, economics, healthcare, and so on. Now, let’s learn a few real-life applications of percentages.

• Percentages help students understand money. For example, banks use percentages to calculate interest on savings and loans, and investors use them to figure out profits or returns. Knowing percentages helps make smarter financial decisions.
   
• In economics, it is used to measure the change in the price, rates of inflation, and unemployment, and to analyze data.
   
• In schools, percentages are used to calculate attendance, grades in assessments, exams, and so on. For instance, if you scored 45 out of 50, your percentage is 90%. Percentages help track progress over time.
   
• When you go shopping, percentages help you save money. Percentages are also used to calculate sales tax, so you know the total cost. A “30% off” sign means you pay only 70% of the price.
   
• Percentages are used to track calories, nutrients, or body weight changes. Lab results often show percentages too, like cholesterol levels, helping doctors and patients understand health better.

Percentile is used to analyze and compare the data for studies. In this section, we will learn more about the real-life application of percentile. 

• Percentile is used in education to compare the score of a student with compare to the whole class. or example, if a student is in the 85th percentile in a test, it means they scored better than 85% of the class.
   
• In health, the percentile is used to analyze the growth of a child by comparing it with the growth chart.
   
• Economists use percentiles to compare the income distribution with the income earned. For instance, being in the 90th percentile for income means a person earns more than 90% of the population. Percentiles help compare wealth and inequality in society.
   
• In sports, percentiles are used to measure performance of players. For example, if a runner finishes a race in the 95th percentile, they ran faster than 95% of all participants.