Percentile Formula

Percentile Formula is a method utilized to evaluate an individual’s performance relative to a group. Commonly used for educational purposes, it aids in understanding where an individual’s score ranks compared to others. The formula calculates the percentile score for a given value ‘x’ by dividing the number of scores below ‘x’ by the total number of values in the population.

Throughout this article, we will delve into the mechanics of the percentile formula and provide examples to enhance comprehension.

What is the Percentile Formula?

The percentile formula serves as a tool for precise comparison of specific values against others within a dataset, emphasizing accuracy. It’s important to note the distinction between percentiles and percentages: while percentages represent a fraction of the whole, percentiles focus on the ranking of individual values within the entire dataset. In essence, calculating percentiles allows us to gauge the relative position of a particular value by determining the percentage of values below it within the dataset. This distinction is vital in accurately assessing performance or position within a given population.

Percentile Definition 

In statistical analysis, a percentile serves as a metric that denotes the threshold below which a specified percentage of data points within a dataset reside. This measure aids in understanding the distribution of values by pinpointing the boundary below which a certain proportion of observations lie.

Percentile Formula

The percentile formula provides a systematic way to quantify the relative position of a particular value within a dataset. It is expressed as:

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

In this formula, “x” represents the value of interest, while the numerator calculates the count of values below “x” and the denominator represents the total number of values in the dataset. Multiplying this ratio by 100 yields the percentile value, indicating the percentage of values below “x”.

Another formula to find the percentile is given by:

P = (n/N) × 100

Where,

• n = ordinal rank of the given value or value below the number
• N = number of values in the data set
• P = percentile

Percentile Calculation

To calculate a percentile using the percentile formula, follow these steps:

• Collect the dataset containing the values of interest.
• Arrange the dataset in ascending order.
• Determine the total number of observations (N) in the dataset.
• Identify the specific data value (x) for which you want to find the percentile.
• Count the number of data values that are less than the specified value (x).
• Divide the count from step 5 by the total number of observations (N) to obtain the percentile of the given data value.

By following these steps, you can effectively use the percentile formula to determine the percentile of a particular value within a dataset.

Solved Example on Percentile Formula

Example 1: In a set of weight values for individuals (50, 55, 40, 60, 100, 95, 90, 60, 80, 75), what percentile does the weight value 60 represent?

Solution:

Given the dataset: 50, 55, 40, 60, 100, 95, 90, 60, 80, 75.

• Sort the data in ascending order: 40, 50, 55, 60, 60, 75, 80, 90, 95, 100.
• Count the number of values in the dataset that are less than 60, which is 4.
• Determine the total number of values in the dataset, which is 10.

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile = (4 / 10) × 100

= 40

Therefore, the weight value 60 represents the 40th percentile in the given population.

Example 2: Consider the scores obtained by 10 students: 38, 47, 49, 58, 60, 65, 70, 79, 80, and 92. Determine the percentile for the score 70 using the percentile formula.

Solution:

• Count the number of scores below 70, which is 6.
• Determine the total number of scores, which is 10.
• Apply the percentile formula:

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile for the score 70:

= (6/10) × 100

= 0.6 × 100

= 60

Therefore, the percentile for the score 70 is 60%.

Example 3: Consider the population consisting of the following values: 1, 6, 7, 3, 8, and 9. Determine the percentile for the value 6.

Solution:

• Sort the data in ascending order: 1, 3, 6, 7, 8, 9.
• Count the number of values below 6, which is 2.
• Determine the total number of values, which is 6.
• Apply the percentile formula:

Percentile = (Number of Values Below “x” / Total Number of Values) × 100

Percentile for the value 6:

= (2/6) × 100

= (1/3) × 100

= 33.33

Therefore, the percentile for the value 6 in the given population is 33.33%.