How to Interpret Standard Deviation and Standard Error in Research

Standard Deviation 101

When it comes to aggregating market research, many of us are fairly familiar with mean, median, and mode. However, one lever deeper on the mean specifically brings us to standard deviation and standard error. Standard deviation specifically offers a variety of insights when it comes to analysis; in business, a standard deviation might imply how risky a venture is. In manufacturing, the standard deviation might reference quality control. So, while standard deviation and standard error are not the most common variables, they’re instrumental in analyzing the confidence surrounding data and results.

What is standard deviation?

Standard deviation is a valuable research tool as it tells how spread out data is. Standard deviation is a value of how far each data point is from the mean, and it is also a descriptive statistic. Descriptive statistics, not surprisingly, describe the features of a data set. This includes values like distribution, mean, median, mode, and variability. Standard deviation helps summarize data, and a high standard deviation signals lots of variability in data. Standard deviations create the famous bell curves of data.

“Focusing on the central tendency in data and not considering its diversity can be disastrous. Unless the average is close to 0% or 100%, we can’t assume that the average represents everyone. In fact, it could represent no one. Does a mediocre rating mean that most people think your offering is mediocre, or do some think it’s great while others think it’s terrible? Can you build a business around just the ones who think it is great? Understanding the standard deviation and standard error helps you to identify opportunities you might otherwise overlook.”

– Nelson Whipple, GreenBook’s GRIT Research Director

Real-life applications of standard deviation

Standard deviation is not just a mathematical term used for research; it’s often used in everyday, real-life situations. From academic studies to business and finance to weather forecasting and medicine, standard deviation is a useful concept beyond the context of research.

Population traits

For example, if looking at population traits like height, weight, or IQ, standard deviation creates a bell curve of the data. If the mean IQ is 100, and the standard deviation equation gives us a value of 10, then we know that roughly ⅔ of the population has an IQ between 90 – 110. The remaining majority of the population would lie in more than one standard deviation of the mean, giving them an IQ of anywhere from 80 – 120.

Financial analysis

Another real-life application is in finance. When it comes to measuring the returns of different financial assets like stocks, bonds, commodities, and real estate, the standard deviation can illustrate how volatile or risky an investment might be.

For example, Stock A and Stock B might have the same annual rate of return of 7%; however, when looking at the standard deviation, Stock A is 2%, and Stock B is 7%. As Stock B has more data points that fall farther from the mean, an investor might receive wildly different returns year to year, making it a more volatile investment. On the other hand, stock A would most likely have an average rate of return that is close to 7% every year!

How to calculate standard deviation

It’s not simple to calculate standard deviation by hand as it uses an advanced equation: (image here). However, free online calculators like this one make it simple to plug in the values and quickly see a standard deviation number.

What is standard error?

Standard error is a value of multiple populations and sample sizes. When taking multiple samples, eventually, all data will be aggregated around a true population mean. The standard deviation of this distribution becomes your standard error. Standard error lets researchers know how accurate a sampling of the population is. For example, if you took the standard deviation of five different samples, you’d be able to see various samples that fell outside the norm. Maybe a sample was biased in some way or failed to hit the normal level of accuracy.

Standard deviation vs. standard error

What’s the difference between standard deviation and standard error? While closely related in survey and market research, standard deviation refers to variability within a single sample, while standard error clues researchers across multiple samples. Standard deviation gives you a closer look at an individual sample, while standard error is more useful for multiple sets of data.

“Would you rather know the average increase in property value in your neighborhood or the likelihood that your property’s value will increase by a certain amount? The mean tells you the former, and the standard deviation and standard error help you estimate the latter.”

–  Nelson Whipple, GreenBook’s GRIT Research Director

How to calculate standard error

Similar to the standard deviation, the standard error is tough to calculate by hand, but it involves dividing the standard deviation by the sample size’s square root. Here is the formula, and here is a free online calculator.

When to use standard deviation and standard error

To determine confidence, volatility, and variability of data, standard deviation and standard error are both helpful tools in survey research and market research. To utilize them in your research, check out a free online calculator to quickly do the work for you.