Entrepreneurship can inherently involve assessing and navigating risks. Recognizing the potential for unexpected shifts in key variables – from market dynamics and revenue streams to overhead expenses – can be the determining factor between successful decisions and financial difficulties.
One wa you can prepare for the uncertainties and complexities of running a business is through statistical measures like standard deviation.
What Is Standard Deviation?
In simplest terms, standard deviation is a statistical tool that measures how much individual data points vary from the mean, or average, of a set of data. It’s sometimes abbreviated as SD or the Greek symbol for sigma (Σ).
Whatever the label, a broader standard deviation means numbers in the data set are more spread out and have “greater variability” from the average. If the numbers are all close to the average, the standard deviation is lower.
Standard deviation can be used in many ways. Investors can use it to measure the volatility of investment returns, whereas scientists might use it to understand the reliability of their data or to make inferences about a larger population. Business owners can also use standard deviation in a variety of ways – especially when making predictions.
“If you’re a small business with a call center, you could use standard deviation to understand how many people you should schedule for shifts,” says Peter Peterka, founder and CEO of Six Sigma, an Austin, Texas-based global consulting firm that uses statistical techniques to improve business processes. “If you’re in logistics, you could use it to understand how many delivery drivers you should have.”
Whether you’re aiming to boost your risk management capabilities, increase manufacturing output, decide whether to close a store with slumping sales, or analyze declining customer satisfaction, standard deviation can be useful to support better decision-making.
One way to prepare for the uncertainties and complexities of running a business is through statistical measures like standard deviation.
How to Calculate Standard Deviation and What It Can Tell a Business
Calculating standard deviation by hand can be more complex than most entrepreneurs – not to mention statisticians – have the time for. Fortunately, commonly used spreadsheet programs and accounting software have functions that can make it easy to apply the standard deviation formula to a column of figures.
Here’s an example of how to calculate standard deviation. Company A and Company B both track sales for the first 11 months of the year and use their accounting software to calculate average sales volume (in thousands of units sold) and standard deviation.
Sales Month |
Company A Sales (in thousands of units) |
Company B Sales (in thousands of units) |
January |
1 |
5 |
February |
3 |
5 |
March |
5 |
5 |
April |
9 |
5 |
May |
4 |
6 |
June |
6 |
6 |
July |
8 |
6 |
August |
2 |
7 |
September |
11 |
7 |
October |
7 |
7 |
November |
10 |
7 |
|
|
|
Average: |
6 |
6 |
Standard Deviation: |
3.16 |
.89 |
The two companies have the same average monthly sales for the year, but different standard deviations. Company B’s smaller deviation reveals lower month-to-month volatility, meaning it can more likely rely on more consistent sales. Company A, on the other hand, has more deviation. These swings may be due to predictable seasonal spikes or other reasons worth investigating, analyzing, and preparing for.
Number of Standard Deviations
When using statistics to inform decisions, risk managers often talk about something being a certain number of standard deviations from the mean: one standard deviation from the mean, two standard deviations from the mean, and so on.
This terminology is used to help explain where most of the values in a group of numbers are likely to be found. In turn, this knowledge can help guide business decisions by showing how “typical” or “extreme” the data is. This can reveal insights into whether things are behaving as might be expected or if something is amiss.
One Standard Deviation
In a normally distributed dataset that follows a bell curve, statisticians expect to find 68% of data points within “one standard deviation” of the mean – or a set “distance” above or below the average.
If a store’s monthly sales slump is within one standard deviation of the mean, it’s within the range of normal fluctuations, and the slump is likely not due to a big change that calls for drastic action. The next month's sales may drift back to the previous level without any action taken.
“Sometimes drops in sales shouldn’t be blamed on marketing strategy if the underlying data is naturally very volatile,” says Eric Feigl-Ding, Chair of Public Health and Chief of the COVID Task Force at the New England Complex Systems Institute. “Don’t fault or fire the marketing person this quarter if their drop in sales is within the usual range of a large SD.”
Two Standard Deviations
Usually, roughly 95% of data points will be found within two standard deviations of the mean. This represents a larger “distance” above or below the average, compared to one standard deviation. The remaining 5% of data points are exceptionally higher or lower than the rest.
According to Feigl-Ding, you want at least 95% of your data to fall within two standard deviations. Any data beyond two standard deviations can potentially influence risk-management strategies.
“It means [the import of the data] is significant, [beyond the range] of what is natural,” he says.
If the number of bad reviews has spiked past two standard deviations, for instance, the situation can merit a closer look – maybe there are severe quality issues, for example.
Three Standard Deviations
Moving still further from the norm, 99.7% of data points will usually be within three standard deviations of the average. In short, data three standard deviations from the mean suggests a seismic shift in underlying conditions. A sales slump this far from the mean, for example, is likely due to some externality, like a catastrophic marketing failure or a substantial swing in consumer behavior, well beyond the typical ebb and flow of a sales quarter.
How to Visualize Standard Deviation
Once standard deviation is calculated, it can be plotted against probability to set up a “bell curve,” assuming the data is distributed normally. Normal distribution means data is concentrated around the average, with fewer data points appearing as you move farther away in either direction.
To visualize this, picture a dartboard after a long night of league play. Most of the darts will have landed close to the middle, and a few may have missed the board entirely.
If 1,000 darts are thrown, the average is the bull’s eye, and the standard deviation is three inches beyond the average, we can expect around 682 darts (68.2%) will land within three inches of the center, 954 darts (95.4%) will land within six inches, and 997 darts (99.7%) will fall within nine inches. Significantly more deviation than that likely signals an atypical situation – maybe it’s amateur night.
In the bell curve below, different sections of the dartboard are shown, with negative represented as darts landing left of the bull’s eye and positive as those falling right of the bull’s eye.
Limits of Standard Deviation
The Six Sigma system used by Peterka’s firm is based on quality-improvement work led by Motorola in the 1980s. The manufacturer sought to have no defects within six standard deviations, hence “six sigma.” This is equivalent to reducing the probability of a manufacturing error until 99.99966% of parts were free of defects.
But standard deviation isn’t a crystal ball that's apt for every situation. Here are some limitations.
Standard deviation can't be used in every instance.
At Six Sigma, use of standard deviation in business often targets improving business processes, such as manufacturing. But using statistics to manage essentially creative functions, like research and development, hasn’t been as successful, as these areas tend to be less quantifiable and less standardized, says Peterka.
Similarly, standard deviation from a limited dataset may not always be applicable to the big picture. For example, a business may look at the standard deviation for manufacturing errors in one factory, but its other factories may use different quality production systems. Applying the lessons learned from one area without considering these differences can lead to overlooked inefficiencies and misaligned adjustments. “Standard error” is another measure analysts can use to extrapolate sample findings to a larger population.
Data must be normally distributed in a bell curve.
Standard deviation can be useful only if the data is normally distributed – i.e., it forms a bell curve. If data points are not normally distributed – meaning they’re off-center and, perhaps, favor a specific outcome either above or below the mean – the graph will be tilted in one direction. In this case, standard deviation might not fully capture the nature of the variability in the data, potentially resulting in misleading interpretations or predictions.
Some business decisions are too complex.
Some business decisions may be too complex to understand just by looking at standard deviations. Simply calculating standard deviation may also fail to produce valid insights if two groups of data are correlated in some way. For instance, to craft an appropriate risk management strategy based on results from a store in a slump, a decision-maker would also have to consider other factors, such as weather and seasonality.
When many factors affect a decision, analyzing them can require more than spreadsheets, Feigl-Ding says. He suggests calling in expert help for such decisions.
“Business managers need to work closely with experienced data people who know how to do complex statistical modeling,” he says.
Additionally, a standard deviation calculated by a spreadsheet can’t always be easily or directly interpreted, especially when comparing performance over time, according to Feigl-Ding.
“It should be an approximate or eyeball test only,” he says.
The Takeaway
Standard deviation can alert a business owner to unusual potential outliers or other signals of significant change. This can help point the way to better risk management strategies and solutions for issues like late-paying customers, slow-turning inventory, and weak-performing salespeople.
Images: Getty
A version of this article was originally published on June 27, 2022.
