Standard deviation as a picture
Standard deviation is usually met as a formula and forgotten as one. The picture fixes it: a histogram of your data with the mean drawn in, and bands one and two standard deviations out on each side. The bands turn an abstract spread number into territory you can point at. Most of the data lives inside the first band or two; the values beyond are the exceptions, visible at the chart's edges.
Commute times again: mean 28.15 minutes, sample standard deviation 4.04. One-SD bands run 24.1 to 32.2; two-SD bands run 20.1 to 36.2. Of the twenty commutes, 13 (65%) fall within one SD and 19 (95%) within two, close to the normal curve's 68-95 script. The single 38-minute trip stands outside the two-SD band, exactly the day you would want to ask about.
Why the bands are in the data's own units
Standard deviation is not a percentage or a score; it is a distance in minutes, marks, dollars: the units of the data. That is its practical strength. "Times average 28 minutes, give or take about 4" is a complete planning statement, and it is the mean-plus-SD pair in plain words. Compare spreads across datasets in the same units directly; across different units, divide by the mean first (the coefficient of variation) to get a fair fight.
Quoting bands for heavily skewed data as if they were symmetric territory. On income-like data the mean + 2 SD band extends into fantasy while mean - 1 SD may cross below zero. The bands still compute; the interpretation must lean on the histogram you are looking at, not on the normal script.
Sample or population SD in the graph?
The bands here use the sample standard deviation (dividing by n − 1), the standard choice when your data are a sample from a larger process: commutes so far, standing in for commutes in general. On a complete population the difference is small and shrinks as n grows.
Frequently asked questions
What does the standard deviation band show?
The territory within one (or two) standard deviations of the mean. For roughly bell-shaped data it holds about 68% (or 95%) of values, and the tool reports your data's actual percentages too.
Why is the SD not in percent?
Because it is a distance in the original units: minutes, marks, kilograms. Dividing SD by the mean gives the coefficient of variation, which is the unit-free version for comparing unlike datasets.
My data are skewed. Are the bands wrong?
The computation is fine; the symmetric reading is not. On skewed data, report the median and quartiles alongside, and read the bands off the histogram itself rather than the normal benchmarks.