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Commute time calculations help us understand the variability in people's daily travel times. In our example with Boston, the average commute time is 27.3 minutes. This 'average' is called the mean. Knowing the mean alone isn’t very helpful because not everyone has the same commute time. Here's where calculations come in handy.
When we talk about commute times within certain ranges, we're essentially looking at how much most people's travel times vary around the average. Calculations like these are important for city planning, road traffic management, and even just for individuals to plan their day better. By considering these ranges, we can find out how many people spend roughly the same amount of time commuting. By using standard deviations, we can break down these times into more digestible and practical information.

A standard deviation is a measure of how spread out commute times—or any other data—are from the average. In simpler words, it tells us whether most people have commute times close to the mean (average) or if they vary widely. In the Boston example, the standard deviation is 8.1 minutes.
Here’s how we use it:

• If you go 1 standard deviation away from the mean (plus or minus), you cover many commute times close to the average.
  That range covers from 27.3 - 8.1 = 19.2 to 27.3 + 8.1 = 35.4 minutes.
• At 2 standard deviations away (from the mean), you capture even more—showing 27.3 - 16.2 = 11.1 to 27.3 + 16.2 = 43.5 minutes.
• For 1.5 standard deviations, calculate 27.3 ± 1.5 * 8.1 to get around 15.15 to 39.45 minutes.

Standard deviations are used for consistency in analysis, and they can help identify unusual data points, like extremely long commute times.

To understand data properly, especially for something as variable as commute times, you need to know two basic things: the mean and the standard deviation. The mean (27.3 minutes in our case) tells us the average commute time. It's what most people experience.
However, the mean alone doesn't tell the whole story. Some people have commute times much shorter or longer.
Here's where the standard deviation (8.1 minutes) comes into play. It complements the mean by showing how much the commute times vary around this average. So, when you hear about distances from the mean like 'within 2 standard deviations' or '1.5 standard deviations,' they are simply referencing how much variation there is in the commute times.
Together, the mean and standard deviation help to paint a complete picture, allowing us to say things like 'at least 75% of people have commute times within 2 standard deviations of the mean' thanks to Chebyshev's Theorem. This helps in planning better routes, adjusting work schedules, and improving overall commuter satisfaction.