How to Find Percentile in Statistics? (original) (raw)
Last Updated : 23 Jul, 2025
A percentile is a statistical measure that indicates the relative standing of a value within a dataset. For example, if a student scores in the 90th percentile on a test, they have scored better than 90% of the other students who took the test.
What are Percentiles?
Imagine a bunch of data points, like test scores. Percentiles help us see how scores are spread out.
In statistics, a percentile is a measure used to indicate the value below which a given percentage of observations in a group of observations fall.
General Formula of Percentile
For calculating the percentile of 'x' in the data,
Percentile = (Number of values below 'x'/Total number of values) × 100
Percentiles are a type of quartile obtained by adopting a subdivision into 100 groups. The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2), and the 75th percentile as the third quartile (Q4). For example, the 50th percentile (median) is the score below (or at or below, depending on the definition) which 50% of the scores in the distribution are found.
**Note: To find the rank or the number of percentile we can modify this formulas as Rank = (Desired Percentile/100) × (n+1).
How to Calculate Percentile?
There are different ways by which we can calculate percentile but the basic idea is to find where that number stands if the total no. of observations were 100.
Here are steps by which we can calculate the value at a given percentile in given data.
**Step 1: Arrange Data
Sort the data set in ascending order.
**Step 2: Calculate Rank
After arranging the data in order, we need to calculate the rank. The formula for rank is given as
Rank = (Desired Percentile/100) × (n+1)
Where n is the number of observations.
**Step 3: Find the Value
- **Case 1: If the rank is a whole number, the value at that position in the ordered dataset is the desired percentile.
- **Case 2: If the rank is a decimal, interpolate to the nearest whole number to find the percentile value.
The general formula to find the Pth percentile is:
P = \frac{100}{n} \times (N+1)
Let's assume we have the following data set: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. To find the 70th percentile:
R = \frac{70}{100} \times (10 + 1) = 7.7
The 70th percentile lies between the 7th and 8th values. Thus, the 70th percentile is a value between 70 and 80.
How is Percentile Useful?
Percentiles are useful because they provide a way to compare individual values to a larger group. There are multiple examples where this is put to use.
- **Competitive Exam: Percentile scores are used in competitive exams to access students as compared to a large pool of students who attempted the exam. For example a 75 percentile indicates that the student scored better than 75% of the students who appeared in the exam.
- **Healthcare: Physicians also use percentile for a child's height and weight to compare with a group of children with similar age and gender. This way doctors can assess how low or high the child's growth is.
- **Traffic Management: Percentile is also used to calculate the speed limit to be set. Usually, the 85th percentile speed of traffic on a road is utilized as a guideline for setting speed limits.
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Solved Questions on Percentile
**Q1: Find the 75 th percentile of the following dataset: 18, 15, 12, 20, 25, 22, 28, 30.
**Solution:
Arrange the data: 12, 15, 18, 20, 22, 25, 28, 30.
Calculate rank:
Rank = (desired percentile/100) × (n+1)
(75/100) × (8+1) = 6.75
Interpolating between the 6th and 7th values due to the rank falling between them.
25 + (28 − 25) × 0.75
= 25 + 3 × 0.75
= 25 + 2.25
= 27.25
The 75th percentile is 27.25.
**Q2: In a class of 50 students, Sarah scored 85 out of 100 on her math test. If Sarah's score is at the 80th percentile, how many students scored lower than her?
**Solution:
Calculate the number of students who scored lower than Sarah.
(80/100) × 50 = 40
So, **40 students scored lower than Sarah.
**Q3: If the 90 th percentile of a dataset is 75, what does it indicate?
**Solution:
It indicates that 90% of the observations in the dataset are below the value of 75.
Practice Questions on Percentile
**Question 1: Calculate the 90th percentile for the following dataset of ages: 25, 28, 30, 32, 35, 38, 40, 42, 45, 50.
**Question 2: In a study of test scores, the following scores were recorded: 75, 80, 85, 90, 95, 100. Determine the 25th percentile of these scores.
**Question 3: A survey collected data on the monthly incomes of individuals in a small town: 1000,1000, 1000,1200, 1500,1500, 1500,1800, 2000,2000, 2000,2200, $2500. What is the 60th percentile income?
**Question 4: The weights of a sample of students were measured in kilograms: 50, 52, 55, 58, 60, 62, 65, 68, 70, 72. Find the 80th percentile weight of these students.
Conclusion
Finding percentiles in statistics is a useful way to understand the distribution of your data. It helps us analyze data and understand where a particular observation stands among a pool of observations in the data.
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