The standard deviation represents how spread out the values are in a dataset relative to the mean.
It is calculated as:
Sample standard deviation = √ Σ(xi – xbar) 2 / (n-1)
Notice the relationship between the mean and standard deviation: The mean is used in the formula to calculate the standard deviation.
In fact, we can’t calculate the standard deviation of a sample unless we know the sample mean.
The following example shows how to calculate the sample mean and sample standard deviation for a dataset in practice.
Suppose we have the following dataset that shows the points scored by 10 different basketball players:
We can calculate the sample mean of points scored by using the following formula:
The sample mean of points scored is 17.6. This represents the average number of points scored among all players.
Once we know the sample mean, we can the plug it into the formula to calculate the sample standard deviation:
The sample standard deviation is 9.08. This represents the average distance between each points value and the sample mean of points.
It’s helpful to know both the mean and the standard deviation of a dataset because each metric tells us something different.
The mean gives us an idea of where the “center” value of a dataset is located.
The standard deviation gives us an idea of how spread out the values are around the mean in a dataset. The higher the value for the standard deviation, the more spread out the values are in a sample.
By knowing both of these values, we can know a great deal about the distribution of values in a dataset.
The following tutorials provide additional information about the mean and standard deviation:
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
Thank you for your very clear and easy to understand definitions and explanations of formulas for mean and standard deviations of data sets. I actually took a college course on the subject, but never understood anything. I failed horribly. I love doing medical research but often don’t understand the clinical research that I find. I can really appreciate a simple explanation that gets me back to the article that I was reading.
James Carmichael says:
Hi Krista…You are very welcome! We appreciate your support and feedback!Statology makes learning statistics easy by explaining topics in simple and straightforward ways. Our team of writers have over 40 years of experience in the fields of Machine Learning, AI and Statistics. Learn more about our team here.
Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student.
Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. Get started with our course today.
