The difference between a percentage and a percentile is that a percentage refers to a numerical figure given out of 100, while a percentile is the proportion of values below a certain value. The % is a tool for quantity comparison. Whereas the position or rank is displayed using a percentile.

Table of Contents

- 1 What is Percentage?
- 2 What is Percentile?
- 3 What is the Difference Between Percentage and Percentile?
- 4 Percentage and Percentile Formulas
- 5 Application of Percentage and Percentile in Real Life
- 6 Similarities Between Percentage and Percentile
- 7 Questions for Practice on Percentage and Percentile
- 8 FAQ’s

## What is Percentage?

A percentage in mathematics is a value or ratio that is given as a fraction of 100. The per cent symbol is commonly used to indicate it, but other acronyms such as pct, pct, and occasionally pc are also used. This table lists key points related to percentages, including definitions, formulas, and applications.

Definition | A percentage is a number or ratio that represents a fraction of 100. |

Representation | Percentages are represented by the symbol “%”. |

Examples | 10% = 1/10 fraction- 20% = ⅕ fraction- 50% = ½ fraction |

Dimension | Percentages are dimensionless numbers, meaning they have no physical dimension. |

Formula | Percentage = (Value / Total value) × 100 |

Calculation | To find the percentage of a number, divide the number by the whole and multiply by 100. |

Conversion | Percentages can be represented in decimal or fraction form, such as 0.6%, 0.25%, etc. |

Fraction to Percentage | A fraction can be converted to a percentage by multiplying by 100. |

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## What is Percentile?

A percentile tells you what per cent of scores fall below a certain value. Imagine a class test. Your 50th percentile score (median) means you did better than 50% of your classmates. Percentiles (written as the nth percentile) help rank scores. They’re especially useful for tests where raw scores might not be clear. This table lists the main concepts related to percentiles:

What Is a Percentile? | A percentile in statistics indicates how a score compares to others in the same dataset, often expressed as the percentage of values below a given score. |

How Is Percentile Helpful? | Percentiles provide a meaningful comparison of values. For instance, in standardized tests, percentiles indicate the percentage of test-takers a particular score exceeds. |

How to Calculate Percentile? | Percentiles can be calculated by using a formula that determines a value’s position in an ordered dataset to the total number of values. Alternatively, percentiles can be determined by sorting the dataset and locating the position of a specific value. |

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## What is the Difference Between Percentage and Percentile?

A percentage is a number or rate that is expressed as a fraction of 100. For example, 50% is equivalent to 50/100, or 0.5. Percentiles, on the other hand, are a way of ranking data. A percentile is a number that indicates the percentage of data points that are equal to or less than a certain value. Here we have differentiated both terms on important parameters:

Feature | Percentage | Percentile |

Definition | A mathematical measure indicating a result as a portion of 100 | A number representing the percentage of values below a specific value |

Unit | Percent (%) | n<sup>th</sup> position (e.g., 20th) |

Quartiles | Not applicable | Can be divided into quartiles (25th, 50th, 75th percentile) |

Ratio representation | Possible | Not possible |

Decimal representation | Possible | Not recommended |

Basis for calculation | Individual value | Rank of numbers in a data set |

Focus | Single instance | Comparison between a single case and a group |

Dependence on normal distribution | Independent | Often based on a normal distribution |

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## Percentage and Percentile Formulas

The percentage formula calculates a portion relative to a whole, expressed as a fraction of 100. The percentile formula identifies a position within a dataset. Understanding these is crucial for analyzing data, comparing values, and understanding proportions. Here’s how you can create a table comparing the calculation of percentage and percentile:

Calculation | Formula | Example |

Percentage | Given value ÷ Total value × 100 | If the given value is 25 and the total value is 50, the percentage would be (25 ÷ 50) × 100 = 50%. |

Percentile | Percentage of values below given value | If a student’s score is at the 80th percentile, it means their score is higher than 80% of the other scores. |

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## Application of Percentage and Percentile in Real Life

Percentage and percentile concepts find applications in diverse real-life scenarios, from calculating discounts in shopping to ranking students’ performance in exams. Applications of percentage and percentile in real life typically include:

- Percentages are used everywhere for discounts and sales. A 20% off coupon means you pay 20% less than the original price.
- Percentiles are often used for grades and test scores. A 90th percentile score means you scored better than 90% of the test takers.
- Percentiles are used in health areas like Body Mass Index (BMI). Knowing your BMI percentile tells you how your weight compares to others of your height.
- Percentiles can help with financial planning. Knowing what percentile your income falls into can help you understand your financial standing compared to others.

## Similarities Between Percentage and Percentile

Imagine you have a class of 100 students. Percentages and percentiles both help us understand how those students did. Here we have listed some important points:

**Percentage:**Think of it like a slice of pie. 50% is half the pie, 25% is a quarter, and so on. It tells you a portion out of the whole thing (100 students).**Percentile:**This is about ranking. If someone scored in the 80th percentile, they beat 80% of their classmates! So, percentiles tell you where someone stands compared to everyone else.

They’re both like different ways of measuring stuff. Percentage is how much of something you have, percentile is where you are compared to others. Kind of like a pie chart (percentage) vs. a scoreboard (percentile).

## Questions for Practice on Percentage and Percentile

Here are some practice questions on percentage and percentile:

If a shirt is initially priced at Rs 400 and is discounted by 20%, what is the discounted price?

A) Rs 320

B) Rs 360

C) Rs 380

D) Rs 400

Answer: C) Rs 320

If 15% of the students in a class are absent, what percentage of students are present?

A) 75%

B) 80%

C) 85%

D) 90%

Answer: C) 85%

A bookstore sold 120 books in a week. If 30% were fiction, how many non-fiction books were sold?

A) 30

B) 60

C) 70

D) 90

Answer: C) 70

If a car depreciates by 10% each year, what is its value after 3 years if it was originally priced at Rs 20,000?

A) Rs 14,000

B) Rs 16,000

C) Rs 18,000

D) Rs 20,000

Answer: A) Rs 14,000

What is 40% of 250?

A) 100

B) 120

C) 150

D) 200

Answer: C) 150

If a restaurant bill is Rs 800 and you want to leave a 15% tip, how much tip should you leave?

A) Rs 80

B) Rs 100

C) Rs 120

D) Rs 150

Answer: B) Rs 120

If a company’s profit margin is 25% and its revenue is Rs 100,000, what is its profit?

A) Rs 20,000

B) Rs 25,000

C) Rs 30,000

D) Rs 35,000

Answer: B) Rs 25,000

What is 75% expressed as a fraction in its simplest form?

A) 3/4

B) 4/5

C) 5/6

D) 6/7

Answer: A) 3/4

If a smartphone is marked up by 40% and its cost price is Rs 300, what is its selling price?

A) Rs 320

B) Rs 360

C) Rs 400

D) Rs 420

Answer: A) 320

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## FAQ’s

**Is percentile the same as percentage?**

Percentile represents a position within a dataset, while percentage expresses a proportion relative to a whole. They measure different aspects.

**What is the difference between percentage and percentile with example?**

Percentage: 70% of students passed the exam.

Percentile: John’s score is at the 80th percentile, meaning he performed better than 80% of test-takers.

**What is a 75th percentile?**

The 75th percentile indicates that 75% of the data points fall below a specific value in a dataset.

**What percentage is the 95th percentile?**

The 95th percentile represents the value below which 95% of the data points lie in a dataset, a high-ranking position.

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