Standard deviation summarizes how far numerical observations typically sit from their mean. It answers a different question from the mean: not “Where is the center?” but “How spread out are values around that center?” Reporting both can give stakeholders a more useful picture than reporting an average alone. section 4.1.1 section 4.1.2
Figure 4.14 The standard deviation essentially takes an average of the differences from the mean.
The figure connects standard deviation to observations’ differences from the mean, making the idea of spread visible. section 4.1.1
Use standard deviation when the distribution is relatively symmetrical and its center is meaningful. A single spread value cannot establish that the distribution is symmetrical; inspect its shape as well. If there is no meaningful center, a range, median, interquartile range, and distribution plot may communicate the data more responsibly. Standard error answers a separate question: how close a sample mean may be to the population mean. Label any error bars clearly so stakeholders know which measure they show. section 4.1.2 section 4.1.1
Checking a distribution before reporting
Generate a distribution, plot a histogram, and calculate its mean, median, and standard deviation. Describe what the standard deviation says about spread around the mean, then inspect the plot before deciding which statistics to share. The standard deviation alone is not a substitute for checking the distribution’s shape. section 4.1.3 section 4.1.2
