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Difference between Percentage and Percentile is essential in comprehending results from pre-employment tests. A percentage is a computation that provides a ratio out of 100.
- Percentile is a metric that represents the value below which a specified proportion of observations in a group fall.
- Percentage and percentile are both the basic metrics used in everyday life.
- Both method are used to describe quantities, particularly scores or marks.
- It is easier to comprehend percentages as they are commonly used to calculate profit or loss.
- The method is used in a variety of statistics in everyday life.
- A daily dose of vitamins per serving provided on the packaging of food items uses the concept of percentage.
- Percentile is used for displaying rank or position.
- The most popular examination, CAT, uses the concept of percentile.
- The formula for percentage and percentile are as follows:
Percentage = (Value/Total Value)× 100
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Key Terms: Differences between Percentage and Percentile, Percentile, Percentage, Statistics, Quartiles, Ratio, Decimal, Fraction, Percentage Formula, Integers
Percentage
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Percentage is defined as the ratio of two integers, which is used to find the quantity in terms of one hundred. It is denoted by the per cent "%" sign, which is used to indicate that the denominator is 100.
- It is the combination of two words, 'per' and 'cent,' which means 'per hundred' or '/100,' which means 'out of 100.'
- 'Out of' is a mathematical word that means 'divide by.'
- The result is obtained by dividing the given value by the total value and then multiplying by 100.
- Percentages give information on proportions and ratios and help to understand the concept effectively.
When we use percentages instead of fractions with distinct denominators, it is often easier to use and understand differences. It is a simple approach to normalize different values for comparison.
- As a result, the percentage has various uses and is used in a variety of situations, including everyday life.
- For example, 80% signifies 80 out of 100, which may be written as a fraction (80/100) or as a decimal (0.80).
- The percentage formula is given as
Percentage = (Value/Total Value)× 100
How to calculate Percentage?
There are two methods used to calculate percentage which are as follows:
Changing Denominator of Fraction to 100
The changing denominator method involves calculating the value of equivalent fraction such that the resultant value of denominator is 100. The result obtain is the percentage itself.
Example of Changing Denominator of Fraction to 100Example: What will be the percentage of 5/20? 5/20 = 5/20 × 5/5 = 25/100 = 25% |
By Using Unitary Method
Unitary method involves multiplication of fraction with 100 to get the required percentage.
Example of PercentageExample 1: At school, based on our performance, we used to get a percentage at the end of the session. We also used percentages to calculate sales tax. Food packaging also includes the recommended intake of vitamins per serving. It’s a part of our daily lives. Example 2: Banking sector widely used percentages to denote interest rates. The most common example is the annual percentage rate (APR) is a price that you pay on a loan.
Example 3: If a student scores 25 marks in their science exams out of a total score of 50, then he or she has scored 50% aggregate in their science exams. 50% is the percentage scored by the student in the science exam. |
Read More:
| Chapter Related Concepts | ||
|---|---|---|
| Multiplication and Division of Integers | Ratio | Division |
| Rules of Multiplication | Proportional Formula | Number System |
Percentile
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In statistics, a percentile is a percentage of values found below a specific value. In other words, it is a point on a measuring scale at or below which a specified percentage of instances fall.
- It is mostly used in the ranking system.
- Percentiles are used in standardized tests to establish a ranking system of achievement.
- The percentile is relative to other people's test scores, but the percentage reflects your result.
- The concept is used in statistics and for assessing standardized tests.
- The percentile formula is given as,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
- Another formula to find the percentile by rank is given by:
P = (n/N) × 100
P = (nth percentile/100) × Total number of values in the list
Here,
- n = Ordinal rank of the given value or value below the number
- N = Number of values in the data set
- P = Percentile
- Rank = Percentile/100
- Ordinal rank for Percentile value = Rank × Total number of values in the list
How to calculate Percentile?
The process to calculate percentile are as follows:
- First, organise the data in ascending order.
- Determine the number of observations in the given sample space.
- Find the data value for which percentile needs to be calculated.
- Determine the number of values which are smaller than the above data value.
- Lastly, divide the number obtained from the fourth step by the number obtained from the second step.
Example of PercentileExample: Suppose a student obtained 65 marks in an exam and this marks is higher than or equal to marks of 85% of the students who gave the exam, then the percentile rank of the student would be 85. |
Difference between Percentage and Percentile
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The difference between percentage and percentile are as follows:
| Percentage | Percentile |
|---|---|
| Percentage is a mathematical unit of measurement that gives a result out of 100. | Percentile is a figure which is used to calculate the values of percentages below it. |
| The percentage does not have quartiles. | The formula have quartiles |
| It is denoted by “%”. | It is denoted by “xth”. |
| Formula can be written as a ratio and also in the form of decimals. | The concept is neither be written as a ratio nor in the form of decimals. |
| The percentage is not based on rank numbers. | Percentile is based on rank numbers. |
| It does not rely on a normal distribution. | It rely on a normal distribution |
| Percentage is based on one case. | Percentile is based on a comparison of one case with all the cases in a particular situation. |
Difference between Percentage and Percentile
Read More:
| Class 7 Mathematics Related Concepts | ||
|---|---|---|
| Comparison of Ratios | Percentage Increase Decrease | Percent Error |
| Ratio To Percentage | Loss Percentage Formula | Profit and Loss Formula |
Things to Remember
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- The difference between percentage and percentile is based on the criteria of ranking.
- Change fraction into a percentage, divide the numerator by the denominator and multiply the result by 100.
- The percentage is a mathematical quantity that is rarely used as a statistical variable.
- Percentile is an essential criterion in entrance exams since it allows institutions to evaluate how candidates perform.
- Percentages do not have quartiles, while percentiles have as they are at the ¼ and ¾ positions on the curve.
- The "%" sign, which means division by 100,' is used to represent a percentage.
- Conversely, the percentile is indicated by "pth", where 'p' is an integer.
Sample Questions
Ques. There are 150 students in a class. Out of them, 75 are girls. Find the percentage of girls in the class.? (2 marks)
Ans. Total number of students in the class=150
Girls in the class=75
% of girls in the class=(75 ⁄ 150) × 100 = (7500 ⁄ 150) = 50%
Ques. What is the formula to calculate percentile? (2 marks)
Ans. The percentile of x is the ratio of the number of values below x to the total number of values multiplied by 100. i.e., The percentile formula is:
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
The percentile formula by rank is:
P = (n/N) × 100
Ques. Suppose Arya scored 560 marks in an exam out of 700. Determine the percentage? (2 marks)
Ans. Maximum Marks: 700
Marks Obtained: 560
Percentage: 560/700 x 100 = 80%
Ques. A shopkeeper marks the price of his goods at 40% higher than the original price. After that, he allows for a discount of 10%. What profit or loss does he get? (3 marks)
Ans. Let the Cost Price of the goods be 100
Since the shopkeeper marked it 20% higher the price becomes 140.
Later the shopkeeper allows a discount of 10% i.e. 140 – 10 = 130
Since the Shopkeeper sold it for a higher price than the original price he will get a profit.
Profit % = ((Selling Price – Original Price)/Original Price)*100
= ((130-100)/100)*100 = 30%
Therefore, shopkeeper makes a profit of 30%.
Ques. In a plot of 3000 sq. m., only 2500 sq. m. is allowed for construction. What percent of the plot is to be left without construction? (2 marks)
Ans. Percentage of Plot allowed for construction = (2500/3000)*100 = 83.3%
Percentage of Plot not allowed for construction = (500/3000)*100 = 16.6%
Ques. A student multiplied a number by 5/7 instead of 7/5, What is the percentage error in the calculation? (5 marks)
Ans. Let the number be x
Ideally, the Number Multiplied by 7/5 is (7/5)x = 7x/5
Number Multiplied by 5/7 is (5/7)x = 5x/7
Error = (7x/5 – 5x/7) = (49x -25x)/35 = 24x/35
Error % = (Error/True Value)*100
= ((24x/35)/(7x/5))*100
= (24x/35*5/7x)*100
= (120/245)*100
= 48.97%
Ques. Ram gets 35 % of total valid votes in an election. If the total votes were 10000, what is the number of valid votes that Ram got? (1 mark)
Ans. Total number of votes cast = 10000
Ram got 45% of Votes i.e. 35/100*10000 = 35*100
= 3500
Ques.The scores for student are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What is the percentile for score 85? (3 marks)
Ans. Given,
No. of. scores below 85 = 8
Total no. of. scores = 10
The formula for percentile is given as,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Percentile of 85
= (8/10) × 100
= 0.8 × 100 = 80
Ques.The weights of 10 people were recorded in kg as 35, 41, 42, 56, 58, 62, 70, 71, 90, 77. Find the percentile for the weight 58 kg? (3 marks)
Ans. Given,
No. of. Weights below 58 = 4
Total no. of. scores = 10
The formula for percentile is given as,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Percentile of 58
= (4/10) × 100
= 0.4 × 100 = 40
Ques. In a college, a list of scores of 10 students is announced. The scores are 56, 45, 69, 78, 72, 94, 82, 80, 63, 59. Using the percentile formula, find the 80th percentile? (4 marks)
Ans. Ascending order - 45, 56, 59, 63, 69, 72, 78, 80, 82, 94
Find the rank,
Rank = Percentile × 100
Rank = 80 × 100
Rank = 0.08
Find the percentile using the formula,
Percentile = Rank × Total number of the data set
Percentile = 0.08 × 10
Percentile = 0.8
Since it not a whole number, round the number to the nearest whole number i.e. 0.8 = 1
Count the set to reach the above number. It is 1.
Therefore, the 80th percentile is 45
Ques.The scores for some candidates in a test are 40, 45, 49, 53, 61, 65, 71, 79, 85, 91. What will be the score with a percentile value of 60? (4 marks)
Ans. We need to find the score “x” with a percentile of 60 for the given data set.
Thus, No. of. Scores below the value “x” i.e. n =?
Total no. of. Scores i.e. N = 10
Given percentile value, P = 60
The formula for percentile is given as below:
P = (n/N) × 100
Rearranging this formula we get:
n = 60x10/100 = 6
Thus 6th value in the data set i.e. 65 will be the score with 90 percentile.
Ques. A number is reduced by 35%. Its present value is 230. What was its original value? (3 marks)
Ans. Let the number be x
The number reduced by price = x – 35/100*x
x -35/100*x = 230
x(1-35/100) = 230
x(35/100) = 230
x = (230*100)/35
= 657.14
Ques. There are 300 students in a class. Out of them, 165 are girls. Find the percentage of girls in the class? (3 marks)
Ans. Given that,
- Total Number of Students = 300
- Number of Boys = 165
Using the Percentage Formula,
Percentage = (Given Value ⁄ Total Value) × 100
Percentage of Girls = (165/300) × 100 = 55%
Thus, the percentage of girls in the class is 55%.
Ques. Consider the list (30, 40, 90, 60, 70). Find the 40th percentiles of the list given? (2 marks)
Ans. Given list – 30, 40, 60, 90, 70
Ordered list ( ascending order) – 30, 40, 60, 90, 70
Here, N = 5
P= 40
n =?
According to the formula
P = (n/N) x 100
40 = (n/ 5) x 100
n = (40 x 5) / 100
n = 2
So, from the ordered list the 2nd number is 40.
Ques. What is 10% of 400? (2 marks)
Ans. The given number is 400. The 10% of 400 needs to be calculated.
Thus,
10% of 400 = (10/100) x 400
= 4000/100
= 40
Therefore, 10% of 400 is 40.
Ques. If you are the fourth tallest person in a group of 40. What is your percentile height in that group? (2 marks)
Ans. Here, N = 40
n = 16 ( as n is the value below which all other people which are smaller than you will come)
Substituting the value in the percentile formula:
P = (16/40) x 100
P = 40
Thus, the 40 percentile is your height in that group.
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