Excel Skewness Calculator
Calculate statistical skewness of your data directly in Excel format
Skewness Results
Comprehensive Guide: How to Calculate Skewness in Excel
Skewness is a fundamental statistical measure that describes the asymmetry of the probability distribution of a real-valued random variable about its mean. In financial analysis, quality control, and scientific research, understanding skewness helps professionals interpret data distributions beyond simple averages and standard deviations.
What is Skewness?
Skewness measures the extent to which a probability distribution of a real-valued random variable “leans” to one side of the mean. There are three types of skewness:
- Positive skewness: The right tail is longer; the mass of the distribution is concentrated on the left
- Negative skewness: The left tail is longer; the mass of the distribution is concentrated on the right
- Zero skewness: The distribution is perfectly symmetrical (like a normal distribution)
Why Calculate Skewness in Excel?
Excel provides built-in functions for calculating skewness, making it accessible to professionals who may not have advanced statistical software. The two primary functions are:
=SKEW()– For sample data=SKEW.P()– For population data
Step-by-Step Guide to Calculate Skewness in Excel
Method 1: Using Built-in Functions
- Prepare your data: Enter your numerical data in a single column (e.g., A1:A20)
- For sample data:
- Click on an empty cell where you want the result
- Type
=SKEW(A1:A20) - Press Enter
- For population data:
- Click on an empty cell where you want the result
- Type
=SKEW.P(A1:A20) - Press Enter
Method 2: Manual Calculation (Understanding the Formula)
The skewness formula for a sample is:
g₁ = [n/(n-1)(n-2)] * Σ[(xᵢ – x̄)/s]³
Where:
- n = number of observations
- xᵢ = each individual observation
- x̄ = sample mean
- s = sample standard deviation
To calculate this manually in Excel:
- Calculate the mean using
=AVERAGE() - Calculate the standard deviation using
=STDEV.S()(for sample) or=STDEV.P()(for population) - For each data point, calculate (xᵢ – x̄)/s and raise to the power of 3
- Sum all these values
- Multiply by n/(n-1)(n-2) for sample skewness
Interpreting Skewness Values
| Skewness Value | Interpretation | Distribution Shape |
|---|---|---|
| Less than -1 | Highly negatively skewed | Long left tail |
| -1 to -0.5 | Moderately negatively skewed | Moderate left tail |
| -0.5 to -0.1 | Slightly negatively skewed | Slight left tail |
| -0.1 to 0.1 | Approximately symmetric | Normal distribution |
| 0.1 to 0.5 | Slightly positively skewed | Slight right tail |
| 0.5 to 1 | Moderately positively skewed | Moderate right tail |
| Greater than 1 | Highly positively skewed | Long right tail |
Practical Applications of Skewness
Understanding skewness has numerous real-world applications:
1. Finance and Investing
Asset returns often exhibit skewness. Positive skewness in returns is desirable as it indicates a higher probability of extreme positive returns (though with more frequent small negative returns). According to a Federal Reserve study, equity returns typically show negative skewness, while option returns show positive skewness.
2. Quality Control
In manufacturing, skewness helps identify whether a process is producing items that consistently meet specifications. Negative skewness in product dimensions might indicate a tendency to produce undersized items.
3. Medical Research
Biological data often shows skewness. For example, NIH research shows that many clinical measurements like blood pressure and cholesterol levels are positively skewed in populations.
Common Mistakes When Calculating Skewness in Excel
- Using the wrong function: Confusing
SKEW()(sample) withSKEW.P()(population) - Including non-numeric data: Text or blank cells in the range will cause errors
- Small sample sizes: Skewness calculations become unreliable with fewer than 30 data points
- Ignoring outliers: Extreme values can disproportionately affect skewness calculations
- Misinterpreting results: Not understanding that skewness is a relative measure that should be considered alongside other statistics
Advanced Techniques
1. Using Data Analysis Toolpak
- Enable the Toolpak: File → Options → Add-ins → Check “Analysis ToolPak” → Go
- Select Data → Data Analysis → Descriptive Statistics
- Choose your input range and check “Summary statistics”
- The output will include skewness among other statistics
2. Creating a Skewness Histogram
Visualizing skewness can provide better intuition:
- Select your data
- Insert → Charts → Histogram
- Adjust bin sizes as needed
- Add a vertical line at the mean to visualize asymmetry
3. Automating with VBA
For repeated calculations, you can create a custom function:
Function CustomSkew(rng As Range, Optional isPopulation As Boolean = False) As Double
Dim n As Long, i As Long
Dim sum As Double, sumCubed As Double
Dim mean As Double, stdev As Double
Dim zScore As Double
n = Application.WorksheetFunction.Count(rng)
If n < 3 Then
CustomSkew = CVErr(xlErrDiv0)
Exit Function
End If
mean = Application.WorksheetFunction.Average(rng)
stdev = Application.WorksheetFunction.StDev_S(rng)
For i = 1 To rng.Count
If IsNumeric(rng(i).Value) Then
zScore = (rng(i).Value - mean) / stdev
sumCubed = sumCubed + zScore ^ 3
End If
Next i
If isPopulation Then
CustomSkew = sumCubed / n
Else
CustomSkew = (n / ((n - 1) * (n - 2))) * sumCubed
End If
End Function
Comparing Excel Skewness with Other Tools
| Tool | Sample Skewness Function | Population Skewness Function | Visualization Capabilities |
|---|---|---|---|
| Microsoft Excel | =SKEW() |
=SKEW.P() |
Basic (histograms, charts) |
| Google Sheets | =SKEW() |
=SKEW.P() |
Basic (similar to Excel) |
| Python (SciPy) | scipy.stats.skew() |
scipy.stats.skew(..., bias=True) |
Advanced (Matplotlib, Seaborn) |
| R | moments::skewness() |
moments::skewness(..., na.rm=TRUE) |
Advanced (ggplot2) |
| SPSS | Analyze → Descriptive → Descriptives | Analyze → Descriptive → Descriptives | Advanced (built-in plotting) |
Limitations of Skewness
While skewness is a valuable statistical measure, it has limitations:
- Sensitive to outliers: Extreme values can disproportionately influence the calculation
- Not robust: Small changes in the data can lead to large changes in skewness
- Scale-dependent: Skewness is not invariant to scale transformations
- Only measures asymmetry: Doesn't capture other distribution characteristics like kurtosis
- Sample size requirements: Requires sufficient data for meaningful interpretation
Best Practices for Working with Skewness in Excel
- Clean your data: Remove outliers or handle them appropriately before calculation
- Use sufficient data: Aim for at least 30 data points for reliable results
- Combine with other statistics: Always examine skewness alongside mean, median, and standard deviation
- Visualize your data: Create histograms to visually confirm the skewness calculation
- Document your method: Note whether you're calculating sample or population skewness
- Consider transformations: For highly skewed data, consider log or square root transformations
Frequently Asked Questions
Q: What's the difference between SKEW and SKEW.P in Excel?
A: SKEW() calculates sample skewness with a correction for bias, while SKEW.P() calculates population skewness without bias correction. Use SKEW() when your data is a sample from a larger population, and SKEW.P() when you have the entire population data.
Q: Can skewness be negative?
A: Yes, negative skewness indicates that the left tail is longer than the right tail. The mass of the distribution is concentrated on the right side of the figure.
Q: What does a skewness of 0 mean?
A: A skewness of 0 indicates a perfectly symmetrical distribution. In practice, values between -0.5 and 0.5 are generally considered approximately symmetrical.
Q: How does Excel calculate skewness?
A: Excel uses the following formulas:
For samples (SKEW):
g₁ = [n/(n-1)(n-2)] * Σ[(xᵢ - x̄)/s]³
For populations (SKEW.P):
G₁ = (1/n) * Σ[(xᵢ - μ)/σ]³
Where μ is the population mean and σ is the population standard deviation.
Q: What's a good sample size for calculating skewness?
A: While there's no strict rule, statistical practice suggests:
- Minimum 30 observations for basic interpretation
- 100+ observations for reliable results
- 300+ observations for precise estimates
For smaller samples, consider using bootstrapping techniques to estimate skewness.
Conclusion
Calculating skewness in Excel provides valuable insights into the asymmetry of your data distribution. Whether you're analyzing financial returns, quality control measurements, or scientific data, understanding skewness helps you move beyond simple averages to grasp the true shape of your data.
Remember these key points:
- Use
=SKEW()for sample data and=SKEW.P()for population data - Interpret skewness values in context with your specific data
- Combine skewness analysis with visualization for better understanding
- Consider data transformations if your data is highly skewed
- Always report whether you're using sample or population skewness
For advanced statistical analysis, you might eventually need to move beyond Excel to specialized software like R or Python, but Excel's skewness functions provide an excellent starting point for most business and academic applications.