Standard deviation is a statistical tool business owners can use to measure and manage risk and help with many decisions. For a manager wondering whether to close a store with slumping sales, how to boost manufacturing quality or what to make of a spike in bad customer reviews, standard deviation can help craft potent risk management strategies.
“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 Global Six Sigma, an Austin, Texas-based consulting firm that uses statistical techniques to improve business processes.
“If you're in logistics," he adds, "you could use it to understand how many delivery drivers you should have."
In statistics, standard deviation measures how much individual data points vary from the mean or average of a set of data. In business risk management applications, standard deviation helps calculate margins of error in customer satisfaction surveys, the volatility of stock prices and much more.
“Standard deviation is a measure of variation that you can use to make predictions," Peterka says. “If you're going to be making predictions in a business, you need to know what your standard deviation is."
Figuring standard deviation by hand would take a lot of calculations. Fortunately, commonly used spreadsheet software has functions that generate the standard deviation from a column of figures with the click of a mouse.
Standard deviation is sometimes abbreviated as SD. The Greek symbol for sigma is also used as a stand in for standard deviation. By whatever name, a larger standard deviation means greater variability in a set of data.
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. For instance, one standard deviation, two standard deviations and so on.
Statisticians expect to find 68 percent of measurements in a suitable set of data within one standard deviation from the mean. This knowledge can help guide risk management strategies and other business decisions.
For instance, if a store's monthly sales slump is within one standard deviation of the mean, it means it's within the range of normal fluctuations. The slump is not necessarily due to a big change that calls for drastic action such as closing the store. The next month sales may drift back to the previous level without a business owner having to do anything.
“Sometimes drops in sales shouldn't be blamed on marketing strategy if the underlying data is naturally very volatile," explains Eric Feigl-Ding, a statistician and health economist in Harvard University's School of Public Health. “I.e., don't fault or fire the marketing person this quarter if their drop in sales is within the usual range of a large SD."
Within two standard deviations from the mean, 95 percent of measurements will usually be found. Beyond this is the point at which variations can potentially influence risk management strategies. If the number of bad reviews has spiked past two standard deviations, for instance, the situation probably merits a closer look.
“You want 95 percent or higher," Feigl-Ding says. “It means this is significant. This is [beyond the range] of what is natural."
Going still further from the norm, 99.7 percent of measurements will usually be within three standard deviations. That means only 0.3 percent of measurements lying outside three standard deviations are due to normal fluctuations in the data. In short, a measurement that is three standard deviations outside the mean suggests that something major has changed.
Limits of Standard Deviation
The Six Sigma system used by Peterka's firm is based on quality improvement work by Motorola in the 1980s. The manufacturer sought to reduce the probability of a manufacturing error until 99.99966 percent of parts were free of defects. This is equivalent to saying there would be no defects within six standard deviations—six sigma.
Six Sigma has been deployed in countless businesses since then. Standard deviation uses in business today include improving manufacturing and other business processes. However, for example, using statistics to manage essentially creative functions like research and development hasn't been as successful.
Sometimes drops in sales shouldn't be blamed on marketing strategy if the underlying data is naturally very volatile.
—Eric Feigl-Ding, statistician and health economist, Harvard University's School of Public Health
Another limitation is that standard deviation is only valid if the data is normally distributed in a bell curve. That is, when a graph of the data forms a bell shape and the mean or average is in the center of the bell. With some distributions, the mean is off-center and standard deviation is less useful.
Also, while standard deviation can give meaningful insight when all points in a set of data are analyzed, statisticians use other techniques to analyze small samples of large data sets, Feigl-Ding adds.
Some business decisions are too complex to understand just by looking at standard deviations. For instance, to craft an appropriate risk management strategy based on results from the slumping store, a decision maker would have to consider factors such as weather and seasonality. Simply calculating standard deviation may also fail to produce valid insight when two groups of data are correlated in some way.
When many factors affect a decision, analyzing them is beyond the capacity of 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.
And a standard deviation calculated by a spreadsheet can't always be easily or directly interpreted, especially when comparing performance over time, Feigl-Ding cautions.
“It should be an approximate or eyeball test only," he says.
The importance of standard deviation in business lies in the way it can alert a business owner to potentially unusual outliers or signals of significant change. This can help point the way to better risk management strategies and solutions for issues ranging from late-paying customers and slow-turning inventory to weak-performing salespeople.
“For small businesses," says Peterka, “it can cause a lot of problems if you don't understand your standard deviation."
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