How To Calculate Skewness Of Data In Excel

Calculate the skewness of your dataset with precise statistical methods

Comprehensive Guide: How to Calculate Skewness of Data 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. Understanding skewness helps analysts determine whether data is normally distributed or if it leans more toward one tail.

What is Skewness?

Skewness quantifies the extent to which a distribution differs from a normal distribution in terms of symmetry. There are three types of skewness:

• Positive Skewness (Right-Skewed): The right tail is longer; the mass of the distribution is concentrated on the left.
• Negative Skewness (Left-Skewed): The left tail is longer; the mass of the distribution is concentrated on the right.
• Zero Skewness: The distribution is perfectly symmetrical (normal distribution).

Why Calculate Skewness in Excel?

Excel provides built-in functions to calculate skewness efficiently, making it accessible for:

1. Financial analysts assessing risk distributions
2. Quality control professionals evaluating process capabilities
3. Researchers analyzing experimental data
4. Business intelligence teams interpreting customer data patterns

Step-by-Step: Calculating Skewness in Excel

Method 1: Using the SKEW Function (Sample Skewness)

The SKEW function calculates sample skewness by returning the skewness of a distribution based on a sample of the population.

1. Enter your data in a column (e.g., A1:A100)
2. In a blank cell, type =SKEW(A1:A100)
3. Press Enter to get the skewness value

Formula: SKEW(number1,[number2],...)

Limitations: Only calculates sample skewness (uses n-1 in denominator). For population skewness, use SKEW.P.

Method 2: Using the SKEW.P Function (Population Skewness)

The SKEW.P function calculates population skewness by evaluating the entire population data.

1. Select your data range (e.g., B1:B50)
2. Type =SKEW.P(B1:B50) in a blank cell
3. Press Enter to compute population skewness

Formula: SKEW.P(number1,[number2],...)

Method 3: Manual Calculation Using Formula

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

Population Skewness: Σ[(xi - μ)³ / N] / σ³

Sample Skewness: [N/(N-1)(N-2)] * Σ[(xi - x̄)³ / s³]

Where:

• xi = each individual value
• μ = population mean
• x̄ = sample mean
• N = number of observations
• σ = population standard deviation
• s = sample standard deviation

Interpreting Skewness Values

Skewness Range	Interpretation	Distribution Shape
< -1	Highly negative skew	Long left tail
-1 to -0.5	Moderate negative skew	Left tail present
-0.5 to 0.5	Approximately symmetric	Normal distribution
0.5 to 1	Moderate positive skew	Right tail present
> 1	Highly positive skew	Long right tail

Real-World Examples of Skewness

Dataset	Typical Skewness	Example Value	Interpretation
Household income	Positive	2.1	Few very high incomes pull the mean right
Exam scores	Negative	-0.8	Most students score high, few score very low
IQ scores	Near zero	0.1	Designed to be normally distributed
Insurance claims	Highly positive	3.5	Most claims are small, few are extremely large

Common Mistakes When Calculating Skewness

1. Confusing sample vs population skewness: Using SKEW when you should use SKEW.P (or vice versa) leads to incorrect interpretations for your specific dataset context.
2. Ignoring outliers: Extreme values can disproportionately affect skewness calculations. Always examine your data for outliers before analysis.
3. Small sample sizes: Skewness calculations become unreliable with fewer than 30 data points. The sample skewness formula includes adjustments for small samples.
4. Misinterpreting zero skewness: A skewness of zero doesn’t always mean perfect normality – it could indicate a balanced but non-normal distribution.
5. Using ungrouped data: For large datasets, consider creating a frequency distribution first to simplify calculations.

Advanced Applications of Skewness in Excel

Combining with Other Statistical Measures

Skewness becomes more powerful when combined with other statistical measures:

• Kurtosis: Use =KURT() to measure “tailedness” of the distribution
• Standard Deviation: =STDEV.P() or =STDEV.S() to understand data spread
• Mean/Median Comparison: In skewed distributions, mean ≠ median. Calculate both to understand the direction of skew.

Visualizing Skewness with Histograms

Create a histogram to visually confirm your skewness calculations:

1. Select your data range
2. Go to Insert > Charts > Histogram
3. Adjust bin ranges to clearly show the distribution shape
4. Add a vertical line at the mean to visualize the skew direction

Automating Skewness Analysis with Excel Tables

For repeated analysis:

1. Convert your data range to an Excel Table (Ctrl+T)
2. Create calculated columns for mean, standard deviation, and skewness
3. Use structured references in your formulas for dynamic updates
4. Add slicers to filter data and see how skewness changes across segments

Authoritative Resources on Skewness

For deeper understanding of skewness calculations and applications:

NIST Engineering Statistics Handbook – Measures of Shape Brown University – Probability Distributions (Interactive) CDC Principles of Epidemiology – Lesson 3: Measures of Risk

Frequently Asked Questions

Q: What’s the difference between SKEW and SKEW.P in Excel?

A: SKEW calculates sample skewness (uses n-1 in the denominator for bias correction), while SKEW.P calculates population skewness (uses n). Use SKEW when your data is a sample of a larger population, and SKEW.P when you have the complete population data.

Q: Can skewness be negative?

A: Yes, negative skewness indicates the distribution has a longer left tail. This means the mass of the distribution is concentrated on the right side, with extreme values pulling the mean to the left.

Q: How does skewness affect the mean and median?

A: In positively skewed distributions, the mean is typically greater than the median (pulled toward the tail). In negatively skewed distributions, the mean is typically less than the median. In perfectly symmetrical distributions, mean = median.

Q: What’s a good sample size for calculating skewness?

A: While skewness can be calculated with any sample size, results become more reliable with at least 30 observations. For sample sizes below 30, consider using bootstrapping methods or consult a statistician.

Q: How do I calculate skewness for grouped data in Excel?

A: For grouped data:

1. Create a table with class intervals and frequencies
2. Calculate midpoints (xi) for each interval
3. Compute the mean of the grouped data
4. Calculate each (xi – mean)³ term
5. Multiply by frequency and sum
6. Divide by (N * σ³) for population or adjusted denominator for sample