Percentile Calculator

The percentile calculator is helpful when you want to calculate any percentile you need for a data set. You can create a table listing of each 5th percentile for the given data set.

You can either type or copy and paste the data into the calculator. Make sure to separate each number with a comma or a space. Then enter the percentile you want in the find percentile box. If you need a table listing each 5th percentile, check the box for 'create a table of percentiles every 5%'. Finally, click the "calculate" button.

Percentiles

Percentiles divide a data collection into 100 equal parts when arranged in ascending order. The pth percentile is always in the range of 0 and 100.

The basic meaning of percentile is "percent below." So, percentiles (pth percentile) are numbers below which a percentage of the ranked data values lie. In other words, p% of the data set values are less than the pth percentile, and (100 − p)% are greater than the pth percentile.

For example, if the value X in a data set has 60% data values below that, we can say that the value X is the 60th percentile of the data set.

Manual Calculating a Percentile Using a Data Set

You can follow the following steps to calculate the percentile manually.

Step 1: Arrange your data set from the smallest number to the largest number (Ascending order)

Step 2: Determine the locator of the percentile that you need. The locator means the percentile rank in the data set, which is arranged in ascending order. You can use the formula following formula to calculate the locator of the percentile.

Calculate Percentile Locator Formula

$$Percentile\ locator (L)=\left( \frac{p}{100}×(n-1) \right)+1$$

Step 3: Identify the value in the percentile locator as the percentile. When finding the value in the percentile locator, you have to start counting from the smallest value and so on.

If the percentile locator is a whole number, then the percentile is precisely equal to the value in the percentile locator. If the percentile locator is not a whole number and contains decimal values, you can determine the percentile as follows:

1. Round down the percentile locator to the nearest whole number and find the value in that locator.
2. Take the difference between the value in the rounded-down percentile locator and the next value in that percentile locator.
3. Multiply the difference from the decimal part of the original percentile locator.
4. Add the above value to the value in the rounded-down percentile locator.

Example 1

Mary has collected all the program fees for postgraduate diploma courses offered by a Canadian college for business students.

Find the 50th percentile of the above data set.

Solution

As the first step, we will arrange the program fees in ascending order.

CAD 16,000, CAD 18,000, CAD 18,000, CAD 20,000, CAD 21,000, CAD 21,000, CAD 22,000, CAD 23,000, CAD 24,000, CAD 24,000, CAD 25,000, CAD 26,000, CAD 28,000

We will find the 50th percentile locator using the percentile locator formula in the second step.

$$Percentile\ locator (L)=\left( \frac{p}{100}×(n-1) \right)+1$$

$$50^{th}\ Percentile\ locator (L₅₀)=\left( \frac{50}{100}×(13-1) \right)+1=(0.5×12)+1=7$$

Now count the 7th number starting from the smallest number (CAD 16,000) in the arranged data values. The 7th number is CAD 22,000. Therefore, the 50th percentile is CAD 22,000.

$$50^{th}\ Percentile(L₅₀)=CAD\ 22,000$$

Therefore, approximately 50% of postgraduate diploma course program fees fall below CAD 22,000.

The Relationship of Percentiles and Other Position Measures

• 50th percentile is equal to the Median value and the second quartile of the data set.

In the same way, you can build the following important relationships between percentiles and quartiles:

• 25th percentile is equal to the first (lower) quartile of the data set.
• 75th percentile is equal to the third (upper) quartile of the data set.

Therefore, in Example 1, we can build the following relationships:

Median = Second quartile = 50th Percentile (P₅₀) = CAD 22,000

Example 1

Use the same data set Mary has collected for all the program fees for postgraduate diploma courses offered by a Canadian college for business students.

Now, find the following:

• 35th percentile
• 85th percentile

Solution

We have already arranged our data set in ascending order as follows.

CAD 16,000, CAD 18,000, CAD 18,000, CAD 20,000, CAD 21,000, CAD 21,000, CAD 22,000, CAD 23,000, CAD 24,000, CAD 24,000, CAD 25,000, CAD 26,000, CAD 28,000

We will find the 35th percentile locator in the second step using the percentile locator formula.

$$Percentile\ locator (L)=\left( \frac{p}{100}×(n-1) \right)+1$$

$$35^{th}\ Percentile\ locator (L₃₅)=\left(\frac{35}{100}×(13-1)\right)+1=(0.35×12)+1=5.2$$

Now the 35th percentile locator is not a whole number. Therefore, we cannot count and find the percentile as per Example 1.

35th percentile locator is 5.2. It is a decimal number between 5 and 6. So, the 35th percentile must be between the 5th and 6th values in the data set, which is arranged in ascending order.

The 5th value of the data set is CAD 21,000

The 6th value of the data set is CAD 21,000

Since both the 5th and 6th values are equal to CAD 21,000, we are not using the extra steps that we discussed for the percentile locators which are not decimals.

Since the 35th percentile must fall between the 5th and 6th values, the 35th percentile should be CAD 21,000.

35th Percentile (P₃₅) = CAD 21,000

Therefore, approximately 35% of postgraduate diploma course program fees fall below CAD 21,000.

We have already arranged our data set in ascending order as follows.

CAD 16,000, CAD 18,000, CAD 18,000, CAD 20,000, CAD 21,000, CAD 21,000, CAD 22,000, CAD 23,000, CAD 24,000, CAD 24,000, CAD 25,000, CAD 26,000, CAD 28,000

We will find the 85th percentile locator in the second step using the percentile locator formula.

$$Percentile\ locator (L)=\left( \frac{p}{100}×(n-1) \right)+1$$

$$85^{th}\ Percentile\ locator (L₈₅)=\left(\frac{85}{100}×(13-1)\right)+1=(0.85×12)+1=11.2$$

Now the 85th percentile locator is not a whole number. Therefore, we cannot count and find the percentile as per Example 1.

85th percentile locator is 11.2. It is a decimal number between 11 and 12. So, the 85th percentile must be between the 11th and 12th values in the data set, which is arranged in ascending order.

The 11th value of the data set is CAD 25,000

The 12th value of the data set is CAD 26,000

Now we will apply the calculation steps for the percentile locator which is not a whole number.

85th Percentile (P₈₅) = 11th value + The difference between 11th & 12th value × Decimal part = CAD 25,000 + (CAD 26,000 - CAD 25,000) × 0.2 = CAD 25,000 + CAD 200 = CAD 25,200

Therefore, approximately 85% of postgraduate diploma course program fees fall below CAD 25,200.

The Importance of Percentile Calculators

You have probably observed that manually determining the percentile is difficult, as seen in Examples A and B.

A statistics percentile calculator allows you to find the answer with a single click. Because the percentiles calculator completes all of the necessary processes to calculate the percentiles.

To begin, you do not need to sort your percentile calculation data if you use the percentiles calculator. The percentile calculator will arrange your data values in ascending order. When you have a large amount of data, it takes a lot of time and effort to manually sort your data in ascending order.

Second, there is no percentile equation to remember when using a percentile calculator to calculate percentiles. You can get the answer without time-consuming calculations. You don't need to find percentile locators or calculate and find the value in a percentile locator.

If you choose to generate a table of percentiles every 5%, the percentile calculator stats display the 0th, 5th, 10th,..., and 100th percentiles.

The Importance of Percentiles

The percentile computation is crucial in several disciplines, including statistics, data analysis, and academic study. Percentiles are often used in the education and health sectors to illustrate how one person compares to others in a group. For example, if a student has a score in the 65th percentile, that means his or her score is on par with or higher than that of 65% of all other students.

Percentiles can occasionally be used to spot extremely high or low values. Imagine that you have measured the weight of your classmates. Weights less than the 10th percentile are exceptionally low, whereas weights greater than the 90th percentile are extremely high.

Additionally, percentiles are used to assess growth. For example, pediatricians display percentiles for children's height and weight on growth charts. Then, parents can compare their child's development to that of other children.