A Comprehensive Guide to Calculating Skewness in Excel

Methods to Calculate Skewness in Excel

Imagine you’re a data analyst tasked to analyze customer wait times at a popular retail chain. The company is experiencing varied customer satisfaction levels across its stores, and management suspects long wait times at checkout might be a contributing factor.

To address this, they have sampled data on customer wait times from a store over a few days.

Customer wait time dataset. Image by Author

As part of analyzing customer wait times, you’ve realized that calculating the skewness metric will provide useful insights. Here are two methods you could utilize to calculate the skewness metric using Microsoft Excel.

Using the SKEW() function

The function computes the degree of skewness of a sample. Here is the syntax of the SKEW() function:

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

For the SKEW() function, we can include up to 255 parameters, each of which can be a single data point or an array of data points.

For our data in hand, we would enter the following formula in a cell, say F2:

=SKEW(B2:B13)

Calculating the skewness using the SKEW() function. Image by Author

Next, once we press Enter on the cell, we can see the skewness coefficient calculated:

Skewness result. Image by Author

The positive output indicates that the wait times are right-skewed. Before interpreting the value, let’s explore another method to find the skewness metric.

Using the Data Analysis Toolpak

The Data Analysis Toolpak is an additional add-in for Microsoft Excel that helps calculate metrics commonly used in data analytics tasks.

Since this add-in isn’t enabled by default, you must check the top right of your Excel workbook for the Data Analysis icon under the Data tab, as shown below.

Data Analysis ToolPak in Excel. Image by Author

If you don’t see the icon, it hasn't been enabled. To enable it, click on File from the menu and select Options.

Selecting Options from the File Tab. Image by Author

Select Add-ins when the Excel Options dialog box opens.

Select Add-ins from the Excel Options dialog box. Image by Author

Next, select Excel Add-ins in the Manage box at the bottom, and click Go.

Managing Excel add-ins. Image by Author 

Check Analysis ToolPak once the Add-Ins dialog box opens and click OK.

Enabling Data Analysis ToolPak. Image by Author

The Data Analysis icon will be visible under the Data tab now, and you need not repeat this process, as enabling the add-in is a one-time task.

As the first step towards calculating the skewness using the enabled add-in, select the range of data points, including the column header, and click on the Data Analysis icon, as shown below.

Invoking the Data Analysis Toolpak add-in. Image by Author

Next, select Descriptive Statistics from the dialog box and click OK.

Selecting descriptive statistics. Image by Author

You will be prompted with a dialog box, as shown below.

Filling in details for descriptive statistics. Image by Author

The Input Range has been prefilled since we selected it before invoking the add-in. Check the Labels in the first row box, and for the Output Range, we select a cell in the same sheet, say $E$5. Check the Summary statistics box, which includes the skewness metric.

Click OK to see the calculated results in the same Excel sheet.

Descriptive statistics results. Image by Author

That’s it! You’ve calculated the skewness and other useful descriptive statistics in one go.

If you are interested in learning more about the Data Analysis Toolpak, check out our Comprehensive Guide to Using ANOVA in Excel tutorial for another useful example. 

Interpreting the Skewness Results

Now that we have the skewness and other descriptive statistics, we can interpret and uncover some useful insights about the sample of data.

• Right-Skewed Distribution: Using both methods, we get the same value of 1.0128 as the skewness metric calculated for the customer wait times at the retail store, indicating a right-skewed (positively skewed) distribution. This means there are outliers in the data with unusually high wait times.
• Mean versus Median: The mean wait times are higher than the median. This suggests that while most customers experience relatively short wait times, there are many instances where wait times are considerably longer, pulling the average up. So median is probably a better measure of center.
• Business Insights: The mode of the wait times is 5 minutes, the most frequently occurring wait time, and indicates that most customers are served relatively quickly. However, the presence of right skewness and a range of 8 minutes highlights that there are significant variations in wait times. The management should focus on reducing these variations to improve overall customer satisfaction.

Suppose the obtained skewness coefficient is negative — how would your interpretation change? Here’s how we can interpret negative skewness values for customer wait times.

• Left-Skewed Distribution: A negative skewness value would indicate that customer wait times follow a left-skewed distribution, with the tail on the left side of the distribution (the lower values) being longer than the right side.
• Low-Valued Outliers: This would suggest that the bulk of the data is concentrated towards the higher end of the scale, with a few lower outliers of extremely low wait times.
• Business Insights: A negatively skewed distribution of customer wait times could indicate efficient operations for the majority of the time. However, it’s important to explore what factors contribute to the exceptionally low values, as these might reveal efficiencies or operational practices that could be leveraged more broadly to improve overall service.

Keep in mind that Calculating other descriptive statistics that complement the skewness metrics helps us reinforce our findings. This is  a common practice in data analytics.

A Deep Dive Into What the Excel Skewness Functions Are Doing

In most practical applications, particularly those involving general statistical analysis or software tools like Excel, the momental skewness is commonly used due to its robustness and comprehensive nature. It is often the default choice unless specific characteristics of the dataset or analysis goals suggest otherwise.

Momental skewness, also known as the third standardized moment, is a statistical measure used to quantify the asymmetry of a data distribution around its mean.

The theoretical definition calculates this by dividing the third central moment of the distribution, which captures the degree of deviation from the mean cubed, by the cube of the standard deviation. However, when analyzing a sample from a larger population, particularly in practical data analysis scenarios, the derived formula for sample skewness is:

Momental skewness equation. Image by Author

Where:

• n is the number of data points.
• Xi is each individual data point.
• xˉ is the mean of the data points.
• s is the standard deviation of the data points.

Further Reading: Other Kinds of Skewness

Pearson’s skewness coefficients

Pearson’s measures of skewness include two coefficients, using mode and median.

Let's take a look at Pearson’s first coefficient of skewness (mode skewness). It compares the mode to the mean and normalizes this difference using the standard deviation. The formula is given as:

Mode skewness equation. Image by Author

Where:

• xˉ is the mean of the data points.
• s is the standard deviation of the data points.

This version of skewness is least used due to the difficulty in accurately determining the mode in many datasets.

Now let's take a look at Pearson’s second coefficient of skewness (median skewness). It quantifies the asymmetry of a distribution by comparing its median to the mean and scaling the result by the standard deviation. The formula is given as:

Median skewness equation. Image by Author

Where:

• xˉ is the mean of the data points.
• s is the standard deviation of the data points.

Since this measure uses the median, it is less affected by outliers, providing a more robust skewness indicator.

Kelly’s measure of skewness

Kelly’s measure of skewness is based on the data's percentiles. It measures the asymmetry of the distribution based on how the median is positioned between the 10th and 90th percentiles.

The formula for Kelly’s skewness is given by:

Kelly’s skewness equation. Image by Author

Where:

• P90 is the 90th percentile.
• P10 is the 10th percentile.
• P50 is the median (50th percentile).

Kelly’s measure focuses on the tails of the distribution and is useful for understanding the skewness in datasets where extreme values are of particular interest.

Bowley’s measure of skewness

Bowley’s skewness, also known as the quartile skewness coefficient, is a way to measure the skewness of a distribution based on quartiles. The formula for Bowley’s skewness is given by:

Bowley’s skewness equation. Image by Author

Where:

• Q1​ is the first quartile (25th percentile).
• Q2 is the second quartile (median, 50th percentile).
• Q3​ is the third quartile (75th percentile).

This measure is less sensitive to extreme values and provides a robust measure of skewness based on the interquartile range.

Final Thoughts

This tutorial introduced you to multiple definitions and the concept of skewness in data distributions. Using a simple example, we learned multiple methods to calculate skewness in Excel and interpreted the results.

Your learning doesn’t have to stop here.  The beginner-friendly Introductions to Statistics course comprehensively covers commonly used statistical techniques and metrics in data analytics. The Excel Fundamentals track would be excellent for learning more about similar analytical tasks using Excel, and the Excel Formulas Cheat Sheet is also helpful for quick reference.

Happy learning!