How To Calculate Kurtosis And Skewness In Excel

Complete Guide: How to Calculate Kurtosis and Skewness in Excel

Understanding the shape of your data distribution is crucial for statistical analysis. Two key measures that describe distribution shape are skewness (asymmetry) and kurtosis (tailedness). This comprehensive guide will show you how to calculate these metrics in Excel using both built-in functions and manual methods.

Why These Measures Matter

Skewness indicates whether data is concentrated more on one side of the mean. Kurtosis measures whether data is heavy-tailed or light-tailed relative to a normal distribution. These metrics are essential for:

• Financial risk assessment
• Quality control in manufacturing
• Psychometric testing
• Medical research data analysis

Understanding the Concepts

What is Skewness?

Skewness measures the asymmetry of data distribution around the mean:

• Positive skewness: Right tail is longer (mean > median)
• Negative skewness: Left tail is longer (mean < median)
• Zero skewness: Perfectly symmetrical distribution

What is Kurtosis?

Kurtosis measures the “tailedness” of the distribution:

• Mesokurtic: Normal kurtosis (≈3 for population, ≈0 when adjusted)
• Leptokurtic: Higher peak, heavier tails (>3)
• Platykurtic: Lower peak, lighter tails (<3)

Calculating Skewness in Excel

Method 1: Using Built-in Functions

Excel provides two functions for skewness:

1. =SKEW() – For sample data
2. =SKEW.P() – For population data

Function	Syntax	Example	Description
=SKEW()	=SKEW(number1,[number2],…)	=SKEW(A2:A100)	Calculates sample skewness (adjusts for bias)
=SKEW.P()	=SKEW.P(number1,[number2],…)	=SKEW.P(B2:B50)	Calculates population skewness

Method 2: Manual Calculation

For educational purposes, you can calculate skewness manually using this formula:

Skewness = [n/((n-1)(n-2))] × Σ[(xᵢ – x̄)/s]³
Where: n = sample size, x̄ = mean, s = sample standard deviation

1. Calculate the mean (=AVERAGE())
2. Calculate the standard deviation (=STDEV.S() for sample)
3. For each value, calculate (xᵢ – mean)³
4. Sum these cubed deviations
5. Divide by [(n-1)(n-2)] and multiply by n

Calculating Kurtosis in Excel

Method 1: Using Built-in Functions

Excel offers these kurtosis functions:

1. =KURT() – For sample data (excess kurtosis)
2. =KURT.P() – For population data

Important Note About Kurtosis Values

The =KURT() function returns excess kurtosis (kurtosis minus 3), so:

• Normal distribution = 0
• Leptokurtic (>0) = Heavy tails
• Platykurtic (<0) = Light tails

=KURT.P() returns actual kurtosis (normal = 3)

Method 2: Manual Calculation

Population kurtosis formula:

Kurtosis = [Σ(xᵢ – x̄)⁴ / n] / σ⁴
Where: σ = population standard deviation

Sample kurtosis (excess) formula:

Kurtosis = {n(n+1)/[(n-1)(n-2)(n-3)]} × Σ[(xᵢ – x̄)/s]⁴ – 3(n-1)²/[(n-2)(n-3)]

Step-by-Step Excel Implementation

Preparing Your Data

1. Enter your data in a single column (e.g., A2:A101)
2. Ensure no blank cells in your data range
3. For large datasets, consider using Excel Tables (Ctrl+T)

Calculating Descriptive Statistics

Before calculating skewness and kurtosis, compute these foundational metrics:

Metric	Sample Data Function	Population Data Function
Count	=COUNT(A2:A101)	=COUNTA(A2:A101)
Mean	=AVERAGE(A2:A101)	=AVERAGE(A2:A101)
Standard Deviation	=STDEV.S(A2:A101)	=STDEV.P(A2:A101)
Variance	=VAR.S(A2:A101)	=VAR.P(A2:A101)

Using Data Analysis Toolpak

For comprehensive statistics:

1. Enable Toolpak: File > Options > Add-ins > Analysis ToolPak > Go > Check box > OK
2. Data > Data Analysis > Descriptive Statistics
3. Select your input range and output options
4. Check “Summary statistics” and “Confidence Level for Mean”
5. The output will include skewness and kurtosis values

Interpreting Your Results

Skewness Interpretation Guide

Skewness Value	Interpretation	Example Distribution
> 1 or < -1	Highly skewed	Income distribution, housing prices
0.5 to 1 or -0.5 to -1	Moderately skewed	Exam scores, product defects
-0.5 to 0.5	Approximately symmetric	Height, blood pressure

Kurtosis Interpretation Guide

Kurtosis Value	Interpretation	Example
> 3 (or > 0 for excess)	Leptokurtic (heavy tails)	Financial returns, earthquake magnitudes
≈ 3 (or ≈ 0 for excess)	Mesokurtic (normal tails)	IQ scores, height
< 3 (or < 0 for excess)	Platykurtic (light tails)	Uniform distributions, some manufacturing processes

Common Mistakes to Avoid

• Using wrong function type: Mixing up sample (=SKEW) and population (=SKEW.P) functions
• Ignoring data cleaning: Outliers can dramatically affect results
• Small sample sizes: Skewness/kurtosis unreliable with n < 30
• Misinterpreting excess kurtosis: Remember =KURT() subtracts 3
• Non-numeric data: Text or blank cells will cause errors

Advanced Applications

Financial Risk Analysis

In finance, kurtosis helps assess “tail risk”:

• Asset returns often show leptokurtosis (fat tails)
• High kurtosis indicates higher probability of extreme events
• Used in Value-at-Risk (VaR) calculations

Quality Control

Manufacturing uses these metrics to:

• Monitor process stability
• Detect shifts in production quality
• Identify non-normal distributions that may affect control charts

Psychometrics

Test developers analyze:

• Item difficulty distributions
• Test score normality assumptions
• Potential ceiling/floor effects

Comparing Excel to Other Tools

Tool	Skewness Function	Kurtosis Function	Notes
Excel	=SKEW(), =SKEW.P()	=KURT(), =KURT.P()	Easy for basic analysis; limited visualization
R	moments::skewness()	moments::kurtosis()	More statistical options; steeper learning curve
Python	scipy.stats.skew()	scipy.stats.kurtosis()	Powerful with pandas; requires coding
SPSS	Analyze > Descriptive > Descriptives	Analyze > Descriptive > Descriptives	GUI-based; good for social sciences
Minitab	Stat > Basic Statistics > Display Descriptive Statistics	Stat > Basic Statistics > Display Descriptive Statistics	Excellent for quality control applications

Real-World Example: Analyzing Stock Returns

Let’s examine the kurtosis and skewness of S&P 500 daily returns (2010-2020):

Metric	Value	Interpretation
Mean Daily Return	0.032%	Slightly positive average return
Standard Deviation	1.02%	Typical daily movement range
Skewness	-0.28	Slight negative skew (more negative outliers)
Kurtosis	5.12	Leptokurtic (fat tails – more extreme moves than normal)

This analysis reveals that while average returns are slightly positive, the distribution has:

• More frequent small losses than gains (negative skew)
• More extreme movements than a normal distribution (high kurtosis)
• Implications for risk management strategies

Visualizing Your Results

Create a histogram with a normal curve overlay to visualize skewness and kurtosis:

1. Select your data
2. Insert > Charts > Histogram
3. Right-click a bar > Format Data Series > Bin options
4. Add a normal distribution curve using trendline options
5. Compare your distribution shape to the normal curve

NIST Engineering Statistics Handbook: Measures of Shape

Comprehensive government resource on skewness and kurtosis with mathematical derivations and practical examples.

BYU Statistics Lab: Descriptive Statistics

Academic guide from Brigham Young University covering descriptive statistics including shape measures with Excel instructions.

CDC Principles of Epidemiology: Measures of Shape

Centers for Disease Control resource on statistical measures in public health data analysis.

Frequently Asked Questions

Why does Excel’s KURT function return different values than other software?

Excel’s =KURT() function returns excess kurtosis (actual kurtosis minus 3), while some other tools return the absolute kurtosis. To get the same value as tools like R or SPSS, add 3 to Excel’s KURT result.

Can I calculate skewness and kurtosis for grouped data?

Yes, but you’ll need to:

1. Calculate the midpoint of each group
2. Multiply each midpoint by its frequency
3. Use these values in your calculations
4. Adjust formulas for the grouped nature of data

What’s the minimum sample size for reliable results?

While you can calculate with any sample size, results become more reliable with:

• n ≥ 30 for moderate reliability
• n ≥ 100 for good reliability
• n ≥ 1,000 for excellent reliability

For small samples, consider using bias-corrected estimators.

How do I handle missing data?

Options include:

• Listwise deletion: Remove all cases with missing values
• Pairwise deletion: Use available data for each calculation
• Imputation: Fill missing values using mean, median, or regression

In Excel, you can use =IFERROR() or data filtering to handle missing values.

Can I automate these calculations for multiple datasets?

Yes! Create a template with:

1. Named ranges for your data
2. Formulas referencing these named ranges
3. Data validation for input controls
4. Conditional formatting to highlight results

Then use VBA macros to process multiple datasets sequentially.

Final Recommendations

1. Always visualize: Plot your data to confirm what statistics suggest
2. Check assumptions: Many statistical tests assume normal distribution
3. Consider transformations: Log or square root transforms can normalize skewed data
4. Document your methods: Note whether you used sample or population formulas
5. Validate with multiple tools: Cross-check Excel results with R, Python, or statistical software

Pro Tip

Create a custom Excel function using VBA to calculate skewness and kurtosis with your preferred adjustments. This gives you more control over the calculation method and can be reused across workbooks.