Difference between Percentage and Percentile with Examples

Difference between Percentage and Percentile

The two terms percentage and percentile are often confused to be synonyms, but they have totally different meanings in terms of mathematics. Let us define the two and see the difference with the help of examples.

Percentage

Percentage word has a Latin origin as it comes from  ‘per centum’ which means ‘per hundred’. This makes it easy to understand what percentage actually is. It is a quantity that describes the measure of something out of hundred, i.e., it is a ratio of an object with respect to numbers out of hundred.

For example, The marks obtained in a test out of hundred. 

Percentile

Percentile gives an idea of the ranking or position of something. After the percentage is calculated for various values for a group they are arranged in ascending order and the rank of one value over the others is determined.

For example, The rank of a student with respect to the marks obtained by him and other students.

Difference Table of Percentage and Percentile

Examples

Example 1: If Daniel scored 70 marks in Science, 67 marks in Mathematics, 78 in English, 75 in Social Studies and 65 in Hindi (all out of 100). Then what is his percentage for the first term for all subjects in total? 

Solution:

The marks that Daniel has got in the first term are:

Science 70/100, Mathematics 67/100, English 78/100, Social Studies 75/100 and Hindi 65/100.

Actual marks that Daniel scored = 70 + 67 + 78 + 75 + 65 = 355

Total Marks for 5 subjects is 500.

We know,

\text { Percentage }=\frac{\text { Actual Value }}{\text { Total Value }} \times 100 \%

Hence, Daniel’s first term Percentage =\frac{355}{500} \times 100 \%=0.71 \times 100 \%=71 \%

Therefore, Daniel scored 71% in his first term examination.

Example 2: In a class of 10 students, the height is measured. The heights are 156, 145, 157, 148, 142, 140, 152, 139, 163, 159 (in cm). Using the percentile formula, find the percentile for the height 145 cm. 

Solution:

Arranging the given data in ascending order – 139, 140, 142, 145, 148, 152, 156, 157, 159, 163.

The number of heights below 145 cm is 3.

We know,

\text { Percentile }=\frac{\text { Number of values below }^{\prime} n^{\prime}}{\text { Total number of Values }} \times 100

Percentile of height 145 cm =\frac{3}{10} \times 100=3 \times 10=30

Therefore, the percentile of height 145 cm is 30.