Many of us rely on spreadsheets not just for work, but also to keep our lives organized. Whether you use a spreadsheet to track your monthly sales numbers or your daily calorie intake, you could benefit from learning how to calculate standard deviation without whipping out a calculator. Read on to discover the best practices for calculating standard deviation in all your virtual spreadsheets.
The Basics of Standard Deviation
Before we explain how to go about calculating standard deviation, let’s first take a moment to understand what standard deviation is and what it measures. Standard deviation is a value that describes the dispersal of a grouped data set by comparing each data point to the mean, or average, of all the data points. The goal is to quickly gauge how far the points in the data set are from the mean. When interpreting results, a higher standard deviation means that the points are more spread out while a lower value indicates that most data points are quite close to the mean.
The standard deviation equation involves taking the square root of the variance, which is the value that represents the spread between points in a data set. Though you can calculate standard deviation using a formula, it is generally much easier to use Excel or another virtual spreadsheet to make the calculations automatically. This practice will also help lower the amount of human errors that often result from performing manual calculations.
Types of Standard Deviation
There are two types of standard deviation: population or sample. If you want to calculate standard deviation in Excel, you will first need to determine which type will be the most effective for your goals. In this section, we will break down each type of standard deviation and the step-by-step instructions needed to calculate it within Excel.
Population Standard Deviation
Population standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a data set. It is calculated by finding the square root of the variance of the entire population, which is the average of the squared differences between each data point and the mean of the population. Population standard deviation is useful for understanding the distribution of data and determining how much the data points deviate from the mean. In Excel, you can easily calculate population standard deviation using the built-in function STDEV.P.
In mathematical terms, the population standard deviation formula is:
σ=N1i=1∑N(xi−μ)2
where:
- σ is the population standard deviation,
- N is the size of the population,
- xi represents each value in the population, and
- μ is the population mean.
Remember, this formula is used when you're considering a full population, not just a sample from that population. For samples, you would use the sample standard deviation formula, which has a slightly different denominator (N-1 instead of N) to account for the Bessel's correction.
To calculate population standard deviation using the built-in function in Excel, simply follow these steps:
Select a cell and type the following formula: “=STDEV.P(...)” Manually enter the range of cells you would like to analyze in the parentheses or select the range by clicking and dragging to highlight the desired cells. Here’s an example of what the formula will look like filled in: “=STDEV.P(A1:A10)” Press enter.
Sample Standard Deviation
The sample standard deviation is calculated when we have a subset of data from the entire population. It is calculated by taking the square root of the sum of the squared deviations of each data point from the sample mean, divided by the total number of data points minus 1.
On the other hand, population standard deviation is calculated when we have the entire population data. It is calculated by taking the square root of the sum of the squared deviations of each data point from the population mean, divided by the total number of data points.
The key difference between the two is that sample standard deviation is calculated using a smaller subset of data, whereas population standard deviation is calculated using the entire population.
To summarize, sample standard deviation measures the variability of a sample dataset, while population standard deviation measures the variability of an entire population dataset. Below, we list the formula for doing this manually and the Excel formula.
In mathematical notation, the sample standard deviation formula is:
s=n−11i=1∑n(xi−xˉ)2
where:
- s is the sample standard deviation,
- n is the size of the sample,
- xi represents each value in the sample, and
- ˉxˉ is the sample mean. This formula, especially with the (n - 1) denominator, is known as Bessel's correction, and it corrects the bias in the estimation of the population variance and standard deviation. It's important to use this version of the formula when working with a sample of a population to get an unbiased estimate.
To calculate sample standard deviation using the built-in function in Excel, follow these steps:
Select a cell and type the following formula: “=STDEV.S(...)” Manually enter the range of cells you would like to analyze in the parentheses or select the range by clicking and dragging to highlight the desired cells. Here’s an example of what the formula will look like filled in: “=STDEV.S(A1:A10)” Press enter.
Best Practices for Calculating Standard Deviation in Excel
We have compiled a few tips and tricks that should make calculating and utilizing standard deviation values in Excel even easier.
Shortcuts and Data Analysis Tools
Excel and other virtual spreadsheets like Google Sheets typically offer both built-in formulas and data analysis tools. To access built-in formulas in Excel, navigate to the “Formulas” tab and select “Insert Function.” From the list on the side, you can choose “STDEV” for standard deviation, then click and drag to select your desired range of cells.
To access built-in data analysis in Excel, visit the “Data” tab and click “Data Analysis.” Choose "Descriptive Statistics" from the list and select the input range as well as the location for the output. Check "Summary statistics" and click "OK." The output will produce a variety of statistics pertaining to the selected range, including the mean and standard deviation.
Common Errors to Avoid
Perhaps the most common mistake when calculating standard deviation in Excel is using the wrong formula. Remember to input “=STDEV.S(...)” for a sample data set that does not include the entire population. Otherwise, you can input “=STDEV.P(...)” to complete the calculation correctly.
Be precise when selecting the range of data you wish to include as well, but don’t fret over accidentally selecting empty cells as Excel will automatically exclude them from the calculation.
Comparing Multiple Data Sets
Use Excel’s quick calculations to gain a better understanding of the differences between data sets. By comparing the standard deviation values, you can determine which data sets are more or less variable than others. Data sets with higher standard deviation values will be more volatile than those with lower values. To further illustrate these results, consider using Excel’s graphing functions to create scatter plots.
Real-World Examples
Here are two real-life examples of calculating standard deviation in Excel to demonstrate how these methods work.
Example 1: Monthly Sales Let’s say you want to calculate the standard deviation in monthly sales numbers for 2023. In cells A2 to A13, you’ve listed the months of the year. In cells B2 to B13, you’ve listed the sales numbers corresponding to each month.
To calculate the standard deviation of this data set, follow these steps:
Select a fresh cell (maybe B14) and enter the standard deviation formula: =STDEV.P(...) Click and drag to select cells B2 to B13 or manually input the range into the formula: =STDEV.P(B2:B13) Press enter to complete the calculation.
Example 2: Student Scores Assume you have listed the latest test scores for a class of 15 students in cells A2 to A16. To calculate the standard deviation of this data set, follow these steps:
Select a fresh cell and enter the standard deviation formula: =STDEV.P(...) Click and drag to select cells A2 to A16 or manually input the range into the formula: =STDEV.P(A2:A16) Press enter to complete the calculation.
Conclusion
Calculating standard deviation can be a crucial part of gathering the data you need, no matter how you are using Excel spreadsheets. Excel is a great option for calculating aspects of your daily life, such as your financial budget. It can also be a great asset in calculating your business's monthly sales. If you need a more robust spreadsheet to manage large amounts of data easily, Row Zero can help. Row Zero can help with business intelligence, finances, marketing, and more! Give Row Zero a try to manage and gather the data you need efficiently.