Looking to learn how to calculate standard deviation?
In this article, we show you the three simple ways to calculate standard deviation. We also explain a little bit about what standard deviation is and why it could be important and useful to you.
Moreover, we answer some of the frequently asked questions about standard deviation.
Here’s everything we’ll cover in this article:
- What is Standard Deviation?
- Standard Deviation Formula
- How to Calculate Standard Deviation using Formulas By Hand
- Steps for Calculating Standard Deviation in Excel
- Calculating Standard Deviation using an Online Calculator
- Why Standard Deviation is Important to Marketers
- FAQs about Standard Deviation
What is Standard Deviation?
Standard Deviation is the average amount of variation in a set of data points. Simply put:
- It tells you how much a value (or data point) has deviated from the mean value.
- It measures how widely a set of values swing back and forth from the mean.
- Standard deviation is commonly abbreviated as SD and denoted by “σ”.
- When your set of data points or values is far from the mean, this indicates a higher standard deviation. Conversely, a lower standard deviation indicates that your data points are closer to the mean.
What does standard deviation tell you?
- Using standard deviation, you can learn how further away each value is from the mean.
- It is especially useful for normal distributions since the data is symmetrically distributed in normal distributions. In normal distributions, it tells you how far each data point is from the center of the distribution.
- Standard Deviation is often used by investors and financial professionals to measure the volatility of a data set and assess an investment’s level of risk.
- You can tell how volatile an investment is by the number of data points that deviate from the mean. The more the data points deviate from the mean, the more volatile the investment is.
- Likewise, Standard Deviation can help marketers decide on the budget of a marketing campaign based on the standard deviation of the ROI.
What’s the difference between Standard Deviation and Variance?
The Standard Deviation is the square root of the data’s variance.
You calculate the Standard Deviation by taking the square root of the Variance. The more your data points vary, the higher the variance.
How to Find Standard Deviation: The Standard Deviation Formula
Depending on the data you have, the way you calculate standard deviation changes.
- You’ve got one formula that helps you calculate the standard deviation when the data is from a whole population.
- And you’ve got another when the data is from a sample.
#1. Population Standard Deviation Formula
You can calculate the population standard deviation from the data you’ve collected from every member of the population.
Here’s the population standard deviation formula:
Here,
- σ = population standard deviation
- ∑ = sum of
- X = each value
- μ = assumed population mean
- N = number of values in the population
#2. Sample Standard Deviation Formula
Calculate sample standard deviation with the data you’ve collected from a specific sample.
Here’s the sample standard deviation formula:
Here,
- s = sample standard deviation
- ∑ = sum of
- X = each value
- x̅ = arithmetic mean of the observations
- n = number of values in that sample
The above two formulas may seem confusing, so below, we’ve listed the steps to put those formulas to use.
However, you can make it easy on yourself and use an online calculator instead. Jump to this section ↓ where we show you how to calculate the standard deviation using an online calculator.
How to Calculate Standard Deviation using Formulas By Hand
Anyway, here are the steps to calculate the standard deviation using the above formulas:
Step 1: Calculate Your Data set’s Mean Value
First, simply add up all the data points and divide them by the number of data points.
Step 2: Calculate Each Data Point’s Deviation from the Mean
Second, subtract the mean value from each data point to find the deviation from the mean.
Step 3: Square Each Deviation from the Mean
Third, multiply each deviation by itself to square them.
Step 4: Find the Sum of All the Squared Deviations
Next, simply add up all of the squared deviations.
Step 5: Find the Variance
Then, divide the sum of all the squared deviations by n -1 (for a sample) or N (for a population).
Step 6: Find the Square Root of the Variance
Finally, take the square root of the variance to find the standard deviation.
How to Calculate Standard Deviation in Excel
How to compute standard deviation online? If you already use excel as part of your current workflow, you’re in luck! There are 6 formulas in Excel that’ll help you calculate the standard deviation. Here are the formulas or Excel functions:
STDEV (or STDEV.S)
The STDEV (or STDEV.S) is the sample standard deviation formula. Use this formula when you want to calculate sample standard deviation without having to account for any text or logical values. And yes, these formulas will work with the older versions of Excel.
STDEVA
Use this formula when you want to calculate the sample standard deviation but you also want to include text and logical values. All the false logical values will be read as 0 and true logical values as 1.
STDEV.P, STDEVPA, and STDEVP
These are the prebuilt functions you use to calculate the population standard deviation. Also, you can calculate the population standard deviation by applying your sample standard deviations to the larger dataset.
Standard Deviation Excel Formula
Here’s the syntax of the stand deviation formula in Excel for STDEV.S:
STDEV.S (number1,[number2],…)
The STDEV.S function uses the following arguments:
Number 1 (required number argument): The first argument that corresponds to the sample of the population
Number 2 (optional number argument): An optional argument that corresponds to a second sample of the population
How to Calculate Standard Deviation Using an Online Calculator
How do you find the standard deviation quickly? You can use an online standard deviation calculator to find the standard deviation in 3 simple steps. Follow the steps below to quickly find standard deviation:
Step 1: Enter Your Data Set into the Calculator
First, enter your data points or numbers, separated by commas.
Step 2: Select the Correct Standard Deviation
Now depending on whether you want to calculate the population standard deviation or the sample standard deviation, click on the “Population” or “Sample” radio button.
Step 3: Calculate
Finally, click the “Calculate” button to find the standard deviation, variance, mean, sum of squares, and margin of error. Then, click “Clear” instead if you want to clear the data you’ve entered and re-enter the data.
Why is Standard Deviation Important and Useful?
- Standard Deviation is especially useful if you want to know the extent to which your data set is unevenly spread out. It tells you not only how spread out your data is, but also how unevenly distributed it is.
- It’s a superior way to calculate variability because it gives you a better idea of your data’s variability than simpler measures like Mean Absolute Deviation (MAD).
- Standard Deviation is used not only to show variability in a data set but also to show the risks and volatility associated with it.
- Marketers can use standard deviation to show the potential risk and reward of a marketing campaign and make the best possible decisions based on data.
- Investors can better assess the risks associated with an investment by accurately predicting an investment’s rate of return.
Frequently Asked Questions about Standard Deviation
What Does Standard Deviation Tell You?
A standard deviation is a measure of how dispersed the data is in relation to the mean. It indicates the extent of deviation from the mean for a data set as a whole.
What is a Normal Distribution?
It’s a distribution wherein values lie in a symmetrical fashion mostly situated around the mean. In other words, in a normal distribution, data is symmetrically distributed. It shows that data near the mean is more frequent in occurrence than data far from the mean.
What are the Different Measures of Variability?
The 4 main measures of variability are Range, Interquartile Range, Standard Deviation, and Variance.
What is the Difference Between Variance and Standard Deviation?
The main difference is in the units. The standard deviation is in the units of variable you’re looking at while the units of variance are the square of those units.
What is the Empirical Rule?
The Empirical Rule (also referred to as the Three-sigma Rule or 68-95-99.7 Rule) states that 99.7% of data observed in a normal distribution lies within 3 standard deviations of the mean. So, 68% of data falls within one standard deviation, 95% within two standard deviations, and 99,7% within three standard deviations.
Final Thoughts
In most cases, you’d only want to calculate the sample standard deviation. However, although you lose some accuracy, you don’t need to look at every member of the population to get accurate results.
Be sure to try one of the methods listed above! Using an online calculator is the simplest way to calculate standard deviation.
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