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The percentile formula is used when we need to compare the exact values or numbers from the provided data to other numbers.
- Percentile and Percentage are sometimes confused, but they are different concepts.
- A percentage is when the fraction is treated as one term.
- The percentile of a value is the percentage of values that are less than the given values out of the whole set of values.
The example below will help to understand the meaning and difference between percentage and percentile. Let the total marks of an exam are 100, then,
- A student received 100 "percent" if and only if he obtained 100/100.
- A student scored 100 "percentile" if all of the other students (100%) scored less than him.
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Key Terms: Percentile, Percentile Formula, Ratio, Number, Percentage, Percentage formula, Fraction, Difference between percentile and percentage
What is Percentile?
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Percentile is used in mathematics to easily understand and interpret the given data.
- Percentile is the exact value found in a particular given data set from the below percentage.
- We get the same unit of measurement of percentile in which we have inputted the data set for calculation.
- Percentile usage is very high in our daily lives.
- Ranging from the calculation of marks in a class to the calculation of biometric measurements of a human body.
Also check:
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|---|---|---|
| Percentage Formula | Mass Percentage | Loss Percentage Formula |
| Percentage Yield Formula with Solved Examples | Ratio To Percentage | Real Numbers Formula |
Percentile Formula
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The percentile formula helps in identifying the performance in comparison to others.
- The ratio of the number of values below 'X' to the total number of values is used to determine the percentile of the value 'X'.
- Percentile calculations can be done for weight, income, and many other factors.
The formula for Percentile is given as
| Percentile = (Number of Values Below “X” / Total Number of Values) × 100 |
The percentile formula can also be given as
| P = (n/N) × 100 |
Where
- n is the ordinal rank of the provided value or a value lower than the number.
- N is the number of values in the data set
- P is Percentile
From the above formula, we can also calculate
- Ordinal rank for Percentile value = Rank × Total number of values in the list
- Rank = Percentile/100
Percentile Calculation
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Here are a few steps to using the percentile formula to calculate the percentile.
- Step 1: Arrange the given data set in ascending order.
- Step 2: Count the total number of observations in the given data set.
- Step 3: Determine the data value for which you want to find the percentile.
- Step 4: Count the number of data values that are smaller than the value specified above.
- Step 5: To obtain the percentile of the given data value, divide the number obtained from Step 4 by the number obtained from Step 2.
Solved Examples
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Ques. The scores for students are 30, 45, 51, 53, 66, 68, 71, 77, 86, and 95. What is the percentile for score 68?
Ans. The given scores of the students are 30, 45, 51, 53, 66, 68, 71, 77, 86, and 95.
From the given data, we have
- Number of scores below 68 = 5
- Total number of scores = 10
The formula for percentile is given by,
Percentile of X= (Number of Values Below “X” / Total Number of Values) × 100
Here X = 68
Therefore,
Percentile of 68 = (5/10) × 100 = 50
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 70th percentile.
Ans. The given scores of students are 56, 45, 69, 78, 72, 94, 82, 80, 63, and 59.
First, we have to arrange the data in ascending order i.e.
45, 56, 59, 63, 69, 72, 78, 80, 82, 94
We have to find the score of 70th percentile.
Therefore, we have P = 70
The formula to find the rank is given by
Rank = Percentile ÷ 100
⇒ Rank = 70 ÷ 100 = 0.7
From the percentile formula, we have
Ordinal rank for Percentile value = Rank × Total number of values in the list
⇒ Ordinal rank for Percentile value = 0.7 × 10 = 7
Counting 7 numbers from left to right, we arrive at 80, and we can conclude that all values below 80 come in the 70th percentile. That is, 70% of the values are less than 80.
Therefore, the 70th percentile is 80.
Also check:
| Mathematics Related Concepts | ||
|---|---|---|
| Difference between area and perimeter | List of Integral Formulas | Bodmas Rules |
| Vector Formula | Interest Formula | Polynomials |
Things To Remember
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- Percentile and Percentage are two different concepts.
- In percentage, a fraction is considered as a single term.
- The percentile of a value is the percentage of values in the whole set of values that are smaller than the given values.
- In Percentile calculation 100 is always multiplied by the ratio of a particular value to the total number of values given.
- The calculated Percentile unit is the same as the provided data unit.
- If the n value comes in decimal then remember to round it off to the nearest whole number.
- The data should be always arranged in an ascending manner. Otherwise, the calculated answer will be wrong.
Sample Questions
Ques. The scores obtained by 10 students are 32, 45, 56, 58, 62, 68, 70, 80, 87, 92. Using the percentile formula, calculate the percentile for score 60. (3 Marks)
Ans. Scores obtained by students are already in ascending order. So we don’t have to arrange the dataset.
38, 47, 49, 58, 60, 65, 70, 79, 80, 92
Number of scores below 60 = 4
Using the percentile formula,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Percentile of 60
= (4/10) × 100
= 0.4 × 100 = 40
Therefore, the percentile for the score 60 = 40
Ques. Consider the list (30, 45, 90, 63, 70). Find the 40th percentiles of the list given. (2 Marks)
Ans.
Given list – 50, 45, 60, 25, 30
Ordered list ( ascending order) – 30,45,63,70,90
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 45.
Hence, 45 is the 40th percentile of a given list
Ques. Consider the weights of 8 people (in kgs) {30, 40, 68, 70, 72, 80, 85, 90}. Find the 70th weight percentile from the weight list. (5 Marks)
Ans.
The weights are already arranged in ascending order. So, the given weights list is as follows:
30, 40, 68, 70, 72, 80, 85, 90
Here, N = 8
P= 70
n = ?
According to the formula
P = (n/N) x 100
70 = (n/ 8) x 100
n = (70 x 8) / 100
n = 5.6
Now, n is in decimals, so rounding off to the nearest value we get
n=6
So, from the ordered list the 6th number is 80.
Hence, 80 kg is the 70th weight percentile of a given weight list.
Ques. The no of chocolates each person contained 10 people was recorded as 10, 3, 4, 12, 20, 14, 16, 6, 19, and 5. Find the percentile for below 10. (3 Marks)
Ans.
Given:
First of all, we have to arrange it in ascending order:
So, we obtained no. of chocolates as 3, 4, 5, 6, 10, 12, 14, 16, 19, and 20,
Number of people with chocolates below 10 = 4
Using the percentile formula,
Percentile = (Number of Values Below “x” / Total Number of Values) × 100
Percentile
= (4/10) × 100
= 0.4 × 100 = 40
Therefore, the percentile for below 10 number of chocolates = 40.
Ques. If you are the fourth tallest person in a group of 20. What is your percentile height in that group? (2 Marks)
Ans.
Here, N = 20
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 = (16/20) x 100
P =80
Thus, the 80 percentile is your height in that group.
Ques. The scores for some candidates in a test are 45, 53, 65, 70, 77. What will be the score with a percentile value of 90? (5 Marks)
Ans.
Given scores: 45,53,65,70,77
Here, N = 5
P= 90
n = ?
According to the formula
P = (n/N) x 100
90 = (n/ 5) x 100
n = (90 x 5) / 100
n = 4.5
Now, n is in decimals, so rounding off to the nearest value we get
n=5 ( as the value after the decimal is greater than 5)
So, from the ordered list the 5th number is 77.
Hence, a 77 score is the 90th percentile of a given weight list.
Ques. If a student is ranked six out of ten in a competition, what is the student's percentile rank? (3 Marks)
Ans.
Here, N=10
n=6 ( as n is the total scores below that value, which is 6 in this case)
P=?
Substituting the value in the formula we get,
P= (6/10) x 100
P= 60
So, 60 is the student’s percentile rank in the competition.
Ques. A data set is given as [10, 30, 35, 40, 48, 52, 65, 70, 85, 90]
From the above data set, 52 is in what percentile? (3 Marks)
Ans.
From the given data, first of all, calculate at which position is 52 in the list.
So, 52 is in 6th position.
Here, n=6
N=10
P=?
Substituting the value in the percentile formula:
P = (6/10) x 100
P =60
Thus, 52 is at the 60th percentile in the given data.
Ques. In a pack of nine candies, the only orange candy weighs more than three in the pack and less than the other remaining five.
What is the percentile of the orange candy weight in comparison to the whole pack? (3 Marks)
Ans.
n is calculated as how many values or items are less or equal to that value
So, n =4 in this case as 4 candies are equal to or less than the orange candy weight.
N =9
P=?
Substituting the values in the percentile formula we get,
P= (4/9) x 100
P = 44.44
Hence, the 44.44 percentile is the orange candy weight in comparison to the whole pack.
Ques. If I ranked eight out of ten in a drawing competition, what is my percentile rank? (2 Marks)
Ans.
Here, N=10
n=8 (as n is the total score below that value, which is 18 in this case)
P=?
Substituting the value in the formula we get,
P= (8/10) x 100
P= 80
So, 80 is my percentile rank in the competition.
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