Percentile Calculator

What is Percentile?

A percentile is a statistical measure that indicates the value below which a certain percentage of data falls in an ordered dataset.

If a value is in the Pth percentile, it means P% of the data is less than or equal to that value.

Examples:

Exam Scores: If you are in the 90th percentile, you scored higher than or equal to 90% of test-takers.
Child Growth Charts: If a child is in the 75th percentile for height, 75% of children of the same age have a height less than or equal to that child’s height.

How to Calculate Percentile (Step-by-Step Explanation)

If you're looking to understand how to find the percentile manually, here’s the complete method. Here is the complete method for calculating a percentile manually

Step 1: Arrange the data in Ascending Order

Sort the dataset:

$$ x_0, x_1, x_2, x_3, \dots, x_{n-1} $$

Where:

n= total number of values

Step 2: Calculate the index position (L)

$$ L = \frac{P}{100} \times (n - 1) $$

Where:

P= desired percentile

N= total data points

Step 3: Interpret the Index (𝑟)

Case 1: If 𝑟 is an integer (r)

Percentile=X𝑟

The percentile equals the value at position r.

Case 2: If 𝑟 is not an integer

Interpolate between the surrounding values.
Let:

i = ⌊𝑟⌋ (integer part)
r_f = 𝑟-𝑟_i (fractional part)

Then calculate the percentile value using linear interpolation:

$$ p = x_i + 𝑟_f (x_{i+1} - x_i) $$

Percentile Example:

Find the 3^rd percentile (P =3) of the given dataset:

10, 10, 34, 23, 54, 9

Solution:
Step 1: Sort Data in Ascending Order

9, 10, 10, 23, 34, 54

Total values:
n = 6
Desired percentile:
P = 3

Step 2: Find the Index Position (L):
Formula:

$$ L = \frac{P}{100} \times (n - 1) $$

Substitute the values:

$$ L = \frac{3}{100} \times (6 - 1) $$ $$ L = 0.03 \times 5 $$ $$ L = 0.15 $$

Step 3: Interpolate the Value

Since L=0.15, the percentile lies between position 0 and position 1:

Index 0 → 9
Index 1 → 10

Formula:

$$ \text{Value} = x_i + (L - \lfloor L \rfloor) \times (x_{i+1} - x_i) $$

Where:

Substitute the values:

$$ i = \lfloor 0.15 \rfloor = 0 $$ $$ p = 9 + (0.15 - 0) \times (10 - 9) $$ $$ p = 9 + 0.15 \times 1 $$ $$ p = 9.15 $$

Final Answer: The 3rd Percentile is 9.15

Common Percentiles Used in Statistics

Percentile	Name	Meaning
25th Percentile	Q1 (First Quartile)	25% of values fall below
50th Percentile	Median	Middle value
75th Percentile	3rd (Third Quartile)	75% of values fall below
90th Percentile	—	90% of values fall below this value
95th Percentile	—	95% of values fall below this value
99th Percentile	—	99% of values fall below this value

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Percentile Calculator

How to Use the Percentile Calculator?

What is Percentile?

How to Calculate Percentile (Step-by-Step Explanation)

Step 1: Arrange the data in Ascending Order

Step 2: Calculate the index position (L)

Step 3: Interpret the Index (𝑟)

Percentile Example:

Common Percentiles Used in Statistics

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