Calculate Tertiles In Excel

Calculate first, second, and third tertiles from your dataset with precise statistical methods. Upload or input your data below.

Complete Guide to Calculating Tertiles in Excel (Step-by-Step)

Tertiles are statistical values that divide a dataset into three equal parts, each containing approximately one-third of the observations. They are particularly useful in data analysis, market research, and academic studies for understanding data distribution and creating meaningful segments.

Why Use Tertiles?

Unlike quartiles (which divide data into four parts) or percentiles (100 parts), tertiles provide a balanced three-way split that:

• Creates low, medium, and high groups naturally
• Works well with normally distributed data
• Provides more granularity than median splits
• Is commonly used in epidemiological studies and social sciences

Understanding Tertile Calculation Methods

There are two primary methods for calculating tertiles, each with different applications:

1. Exclusive Method (Default):

   This method excludes the tertile values themselves from the groups. For example, with tertiles at 20 and 40:

   • First group: Values below 20
   • Second group: Values between 20 and 40
   • Third group: Values above 40
2. Inclusive Method:

   This method includes the tertile values in the lower group. Using the same example:

   • First group: Values ≤ 20
   • Second group: Values > 20 and ≤ 40
   • Third group: Values > 40

Step-by-Step: Calculating Tertiles in Excel

Method 1: Using PERCENTILE.EXC Function (Recommended)

1. Prepare Your Data:

   Enter your dataset in a single column (e.g., A2:A101). Ensure there are no blank cells in your range.

2. Calculate First Tertile (33.33rd percentile):

   In a new cell, enter:
   =PERCENTILE.EXC(A2:A101, 1/3)

3. Calculate Second Tertile (66.67th percentile):

   In another cell, enter:
   =PERCENTILE.EXC(A2:A101, 2/3)

4. Verify Your Results:

   Count how many values fall below each tertile to ensure they represent approximately 1/3 of your data.

Method 2: Using PERCENTILE.INC Function

For the inclusive method, use:

• =PERCENTILE.INC(A2:A101, 1/3) for first tertile
• =PERCENTILE.INC(A2:A101, 2/3) for second tertile

Pro Tip:

For large datasets, consider using Excel’s Data Analysis ToolPak (under Data tab) for more advanced statistical analysis including tertiles, quartiles, and percentiles.

Advanced Tertile Applications in Excel

Creating Tertile Groups

To categorize your data into tertile groups:

1. Calculate your tertile values as shown above
2. Use the IF function to create groups:

   =IF(A2<$T1,"Low",
                        IF(A2<$T2,"Medium","High"))

   Where T1 and T2 are cells containing your tertile values
3. Use conditional formatting to visually distinguish the groups

Tertiles vs. Other Statistical Measures

Measure	Divisions	Excel Function	Best Use Case
Tertiles	3 equal parts	PERCENTILE.EXC/INC	Three-group comparisons, normal distributions
Quartiles	4 equal parts	QUARTILE.EXC/INC	Four-group comparisons, box plots
Quintiles	5 equal parts	PERCENTILE.EXC/INC	Five-group comparisons, detailed segmentation
Deciles	10 equal parts	PERCENTILE.EXC/INC	Ten-group comparisons, detailed analysis
Percentiles	100 equal parts	PERCENTILE.EXC/INC	Precise ranking, standardized tests

Common Mistakes When Calculating Tertiles

1. Using Sorted vs. Unsorted Data:

   Excel's percentile functions work on the actual values, not their position. Always ensure your data is properly sorted when verifying results.

2. Ignoring Ties:

   When multiple identical values exist at the tertile boundary, decide whether to include them in the lower or higher group based on your analysis needs.

3. Small Sample Size:

   With fewer than 6-9 data points, tertiles become less meaningful. Consider using quartiles or median splits instead.

4. Mixing Methods:

   Be consistent with either EXC or INC functions throughout your analysis to avoid inconsistent grouping.

Real-World Applications of Tertiles

Tertiles are widely used across various fields:

Field	Application	Example
Education	Student performance grouping	Low, medium, high achieving students
Healthcare	Risk stratification	Low, medium, high risk patients
Marketing	Customer segmentation	Low, medium, high value customers
Finance	Income distribution analysis	Low, middle, high income groups
Environmental Science	Pollution level categorization	Low, medium, high pollution areas

Excel Shortcuts for Tertile Analysis

• Quick Sort: Select your data and press Alt + D + S to sort
• AutoSum: Alt + = to quickly sum tertile groups
• Format as Table: Ctrl + T to easily analyze tertile groups
• Pivot Tables: Alt + N + V to create tertile-based pivot tables

Alternative Methods for Calculating Tertiles

Using Array Formulas

For more control over the calculation:

=PERCENTILE(INDIRECT("A2:A" & COUNTA(A:A)), 1/3)

Using Power Query

1. Load your data into Power Query
2. Add a custom column with formula:

   if [Column1] <= T1 then "Low" else if [Column1] <= T2 then "Medium" else "High"

3. Load back to Excel for analysis

Using VBA Macro

For automated tertile calculation across multiple sheets:

Sub CalculateTertiles()
    Dim ws As Worksheet
    Dim rng As Range
    Dim T1 As Double, T2 As Double

    Set ws = ActiveSheet
    Set rng = ws.Range("A2:A" & ws.Cells(ws.Rows.Count, "A").End(xlUp).Row)

    T1 = Application.WorksheetFunction.Percentile_Exc(rng, 1/3)
    T2 = Application.WorksheetFunction.Percentile_Exc(rng, 2/3)

    ws.Range("B1").Value = "First Tertile"
    ws.Range("C1").Value = "Second Tertile"
    ws.Range("B2").Value = T1
    ws.Range("C2").Value = T2
End Sub

Authoritative Resources on Tertiles

• NIST/Sematech e-Handbook of Statistical Methods - Quantiles
• UC Berkeley - Understanding Quantiles and Tertiles
• CDC - Public Health Statistics: Quantiles and Tertiles

Frequently Asked Questions About Tertiles

How do tertiles differ from quartiles?

Tertiles divide data into 3 equal parts (33% each) while quartiles divide into 4 parts (25% each). Tertiles provide a middle ground between the simplicity of median splits and the granularity of quartiles.

Can I calculate tertiles for non-numeric data?

No, tertiles require numeric data since they're based on the numerical order of values. For categorical data, consider frequency distributions instead.

What's the minimum sample size for meaningful tertiles?

While technically possible with any sample size, tertiles become statistically meaningful with at least 9-12 data points (3-4 per group). For smaller datasets, consider median splits.

How do I handle tied values at tertile boundaries?

This depends on your analysis needs:

• Exclusive method: Place tied values in the higher group
• Inclusive method: Place tied values in the lower group
• Alternative: Distribute tied values proportionally between groups

Can I calculate tertiles in Excel Online?

Yes, the same functions (PERCENTILE.EXC and PERCENTILE.INC) are available in Excel Online with identical syntax.

Final Thoughts on Using Tertiles in Excel

Mastering tertile calculation in Excel opens up powerful analytical capabilities for segmenting and understanding your data. Remember these key points:

• Choose between exclusive and inclusive methods based on your analysis requirements
• Always verify your tertile calculations by counting values in each group
• Consider visualizing your tertile groups with conditional formatting or charts
• For large datasets, automate the process with VBA or Power Query
• Document your tertile calculation method for reproducibility

By incorporating tertiles into your Excel workflow, you'll gain deeper insights into data distribution and create more meaningful data segments for analysis and reporting.