How To Calculate 25Th And 75Th Percentile In Excel

Calculate 25th and 75th percentiles from your data with step-by-step results

Percentiles are statistical measures that indicate the value below which a given percentage of observations fall. The 25th percentile (first quartile) and 75th percentile (third quartile) are particularly important as they help define the interquartile range (IQR), which measures statistical dispersion and is often used to identify outliers.

Understanding Percentiles in Statistics

Before diving into Excel calculations, it’s essential to understand what percentiles represent:

• 25th Percentile (Q1): The value below which 25% of the data falls
• 50th Percentile (Median/Q2): The value below which 50% of the data falls
• 75th Percentile (Q3): The value below which 75% of the data falls
• Interquartile Range (IQR): Q3 – Q1, representing the middle 50% of data

The IQR is particularly useful because it’s less sensitive to outliers than the range (max – min). Data points that fall below Q1 – 1.5×IQR or above Q3 + 1.5×IQR are typically considered outliers.

Excel Functions for Percentile Calculation

Excel provides two main functions for calculating percentiles:

PERCENTILE.INC

Inclusive method that includes all data points in calculations. The formula is:

=PERCENTILE.INC(array, k)

Where:

• array is your data range
• k is the percentile value (0.25 for 25th, 0.75 for 75th)

PERCENTILE.EXC

Exclusive method that excludes the min and max values. The formula is:

=PERCENTILE.EXC(array, k)

Where:

• array is your data range
• k is the percentile value (0.25 for 25th, 0.75 for 75th)

Note: PERCENTILE.EXC requires at least 2 data points and k must be between 0 and 1 (exclusive).

Key Differences Between INC and EXC

Feature	PERCENTILE.INC	PERCENTILE.EXC
Includes endpoints	Yes	No
Minimum data points	1	2
k value range	0 to 1 (inclusive)	0 to 1 (exclusive)
Common use cases	General percentile calculations	When excluding extremes is desired
Excel 2007 compatibility	No (use PERCENTILE)	No

Step-by-Step Guide to Calculate Percentiles in Excel

1. Prepare your data:

   Enter your numerical data in a single column. For example, place your values in cells A2:A20.

2. Sort your data (recommended):

   While not strictly necessary, sorting makes it easier to verify your results. Select your data range and click the Sort A to Z button on the Data tab.

3. Calculate the 25th percentile:

   In a blank cell, enter one of these formulas:

   =PERCENTILE.INC(A2:A20, 0.25) (inclusive method)

   =PERCENTILE.EXC(A2:A20, 0.25) (exclusive method)

4. Calculate the 75th percentile:

   In another cell, enter:

   =PERCENTILE.INC(A2:A20, 0.75) or

   =PERCENTILE.EXC(A2:A20, 0.75)

5. Calculate the Interquartile Range (IQR):

   Subtract the 25th percentile from the 75th percentile:

   =B2-B1 (assuming 75th is in B2 and 25th is in B1)

6. Format your results:

   Select the cells with your results and use the Number Format dropdown on the Home tab to display the appropriate number of decimal places.

Manual Calculation Method

For those who want to understand how Excel calculates percentiles, here’s the manual method:

For PERCENTILE.INC (n = number of data points, k = percentile):

1. Sort your data in ascending order
2. Calculate the position: P = (n - 1) × k + 1
3. If P is an integer, the percentile is the value at position P
4. If P is not an integer:
• Take the integer part (floor) as position f
• Take the fractional part as c
• Percentile = value at f + c × (value at f+1 – value at f)

Example Calculation:

For data [12, 15, 18, 22, 25, 30, 35, 40, 45, 50] (n=10) and 25th percentile (k=0.25):

1. P = (10-1)×0.25 + 1 = 3.25
2. f = 3 (integer part), c = 0.25 (fractional part)
3. Value at position 3 = 18
4. Value at position 4 = 22
5. 25th percentile = 18 + 0.25×(22-18) = 19

Common Mistakes to Avoid

• Using unsorted data: While Excel’s functions work on unsorted data, manual calculations require sorted data.
• Confusing INC and EXC: These functions can give different results, especially with small datasets.
• Incorrect k values: Remember EXC requires k between 0 and 1 (exclusive).
• Ignoring data format: Ensure all data is numerical (no text or blank cells).
• Not handling duplicates: Percentile calculations work correctly with duplicate values.

Advanced Applications of Percentiles

1. Identifying Outliers

Percentiles are crucial for outlier detection using the 1.5×IQR rule:

• Lower bound = Q1 – 1.5×IQR
• Upper bound = Q3 + 1.5×IQR
• Any data point outside this range is considered an outlier

2. Standardized Test Scoring

Many standardized tests (SAT, GRE) report percentile ranks to show how a score compares to others. For example, a 75th percentile means the test-taker scored better than 75% of participants.

3. Income Distribution Analysis

Economists frequently use percentiles to analyze income distribution. The 25th and 75th percentiles help understand the spread of incomes beyond just the median.

Income Percentiles in the U.S. (2023 Estimates)

Percentile	Individual Income	Household Income
25th	$25,000	$45,000
50th (Median)	$45,000	$75,000
75th	$80,000	$120,000
90th	$120,000	$180,000

Source: U.S. Census Bureau

Excel Alternatives for Percentile Calculation

QUARTILE Function

Excel’s QUARTILE function can calculate specific quartiles:

=QUARTILE(array, quart)

Where quart can be:

• 0 for minimum
• 1 for 25th percentile
• 2 for median
• 3 for 75th percentile
• 4 for maximum

PERCENTRANK Functions

To find what percentile a specific value represents in your dataset:

=PERCENTRANK.INC(array, x, [significance])

=PERCENTRANK.EXC(array, x, [significance])

Visualizing Percentiles with Excel Charts

Box plots (box-and-whisker plots) are excellent for visualizing percentiles:

1. Calculate Q1, median, Q3, min, and max
2. Calculate lower fence (Q1 – 1.5×IQR) and upper fence (Q3 + 1.5×IQR)
3. Create a stacked column chart with:
• Box from Q1 to Q3
• Whiskers from min to Q1 and Q3 to max
• Median line
• Outliers marked individually

For Excel 2016 and later, you can use the built-in Box and Whisker chart type under Insert > Charts > Statistical.

Real-World Applications

1. Healthcare and Medicine

Growth charts for children use percentiles to compare a child’s height/weight to population norms. The CDC growth charts use the 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles.

2. Education and Testing

Standardized tests like the SAT report percentile ranks. A score at the 75th percentile means the student scored better than 75% of test-takers. The College Board provides detailed percentile information.

3. Finance and Economics

Portfolio managers use percentiles to evaluate fund performance relative to peers. Morningstar’s star ratings are based on percentile rankings within categories.

Troubleshooting Common Issues

#NUM! Errors

Common causes and solutions:

• Empty array: Ensure your data range contains at least 1 (INC) or 2 (EXC) numbers
• Invalid k: For EXC, k must be >0 and <1. For INC, k must be ≥0 and ≤1
• Non-numeric data: Remove any text or blank cells from your range

Unexpected Results

If your results seem off:

• Verify your data is sorted (for manual calculations)
• Check for hidden characters or formatting issues in your data
• Compare with manual calculations to identify discrepancies
• Ensure you’re using the correct function (INC vs EXC)

Best Practices for Working with Percentiles

• Document your method: Note whether you used INC or EXC for reproducibility
• Consider your audience: EXC might be preferable when excluding extremes is important
• Validate with small datasets: Test with 5-10 numbers to ensure your approach works
• Use helper columns: For complex analyses, break calculations into steps
• Visualize your data: Always pair percentile calculations with appropriate charts

Learning Resources

For those who want to dive deeper into percentiles and Excel statistics:

• Khan Academy Statistics Course – Free comprehensive statistics education
• Microsoft Office Support – Official documentation for Excel functions
• NIST Engineering Statistics Handbook – Advanced statistical methods