Standard deviation in everyday life
Most everyday planning runs on averages: the commute takes about half an hour, the weekly shop is about $95. The average gets you through a typical day. The standard deviation tells you how much slack to build in for the days that are not typical, and with a week or two of notes you can work it out for your own life.
The commute: leave mean + 1 SD early
Say you time your drive to work for ten days (these numbers are illustrative):
28, 31, 26, 35, 29, 42, 30, 27, 33, 29 minutes
The total is 310, so the mean is 31 minutes. The sample standard deviation is 4.71 minutes; paste the list into the mean and standard deviation calculator to see the working. If you leave 31 minutes before a meeting, you are late roughly half the time, because half of all days take longer than average. That is the practical cost of planning on the mean.
Adding a standard deviation or two changes the odds. If commute times were roughly normal, the share of days you would arrive in time would be:
| Leave this early | Minutes | On time (normal model) |
|---|---|---|
| Mean | 31 | 50% |
| Mean + 1 SD | 35.7 | 84% |
| Mean + 1.5 SD | 38.1 | 93% |
| Mean + 2 SD | 40.4 | 98% |
So for the daily run, leaving 36 minutes ahead keeps you on time about five days out of six. For a job interview or a flight, where being late is expensive, give yourself mean + 2 SD, about 40 minutes, or more.
Real commutes are not quite normal. They have a floor (the road cannot be faster than empty) and a long tail of bad days, like the 42-minute day in this list, which is the only one of the ten beyond mean + 1 SD and also beyond mean + 2 SD. The normal percentages are a guide; for important trips, look at your worst few days as well. The empirical rule calculator shows the bands for any mean and SD.
The SD also helps compare routes. A route averaging 29 minutes with an SD of 9 is worse for a fixed start time than one averaging 32 with an SD of 2: at mean + 2 SD you would need 47 minutes for the first and 36 for the second. The page on standard deviation vs mean covers this kind of comparison more generally.
Try it: mean and standard deviation calculator
The ten commute times are filled in; replace them with your own trips, bills or battery readings to get your mean and SD.
Separate numbers with commas, spaces or new lines, or paste a spreadsheet column.
Decimals and negatives are fine; write 10:3 for a value that occurs 3 times.
Your results will appear here: the standard deviation first, then the rest of the summary and a chart.
Standard deviation (sample)
4.71405
Your values typically sit about 4.71 above or below their mean of 31, in the same units as your data. 8 of 10 values (80%) fall between 26.29 and 35.71, within one standard deviation of the mean; for normally distributed data about 68% would.
Population SD (σ): 4.47214, if these values are the whole group.
- Count (n)
- 10
- Mean (x̄)
- 31
- Variance (s²)
- 22.2222
- Standard error
- 1.49071
- Minimum
- 26
- Q1 (25%)
- 28.25
- Median
- 29.5
- Q3 (75%)
- 32.5
- Maximum
- 42
- Range
- 16
More statistics (5)
- Relative SD (%RSD)
- 15.2066%
- Coefficient of variation
- 0.152066
- Sum (Σx)
- 310
- Sum of squares, Σ(x − x̄)²
- 200
- IQR (Q3 − Q1)
- 4.25
Data distribution
Shaded bands mark ±1, ±2 and ±3 SD from the mean. 8 of 10 values (80%) fall within ±1 SD.
Chart as text
Mean 31, sample standard deviation s = 4.71405, from 10 values between 26 and 42.
- Within ±1 SD (26.29 to 35.71): 8 of 10 values (80%). About 68% for normal data.
- Within ±2 SD: 9 (90%). About 95% for normal data.
- Within ±3 SD: 10 (100%). About 99.7% for normal data.
Show the working, step by step
Open the full mean and standard deviation calculator for the working and more examples.
Grocery bills: budget for the month, not four worst weeks
Eight weeks of illustrative grocery receipts:
$82, $104, $91, $120, $76, $98, $88, $101
They total $760, a mean of $95 a week, with a standard deviation of $13.87. A four-week month averages 4 × $95 = $380. The tempting way to add a cushion is to budget mean + 1 SD for every week, 4 × $108.87 = $435.47. That is more padding than you need, because expensive weeks and cheap weeks tend to cancel out.
If each week's spending is independent of the others, the variances add, not the standard deviations. The SD of a four-week total is √4 × $13.87 = $27.73, not 4 × $13.87. That gives:
| Monthly budget | Amount | Covers (normal model) |
|---|---|---|
| Mean | $380.00 | 50% of months |
| Mean + 1 SD | $407.73 | 84% of months |
| 4 × (weekly mean + 1 SD) | $435.47 | 98% of months |
The “add a weekly SD every week” budget turns out to be the monthly mean + 2 SD. It is a safe budget, but it ties up about $28 a month more than the 84% level. The independence assumption matters: if a big shop one week means a small one the next, the monthly total is even steadier than this; if expensive weeks bunch together, as they do around holidays, it is less steady.
Sleep: the average hides the pattern
Two illustrative weeks of sleep, both averaging just under seven hours a night:
| Week | Hours each night | Mean | SD |
|---|---|---|---|
| Irregular | 7.5, 6.0, 7.2, 8.1, 5.5, 7.0, 6.8 | 6.87 | 0.88 |
| Regular | 6.9, 7.1, 7.0, 6.8, 7.2, 7.0, 6.8 | 6.97 | 0.15 |
A sleep app's weekly average would score these weeks almost the same. The first one includes two nights under six and a half hours and a catch-up night of eight. If you are trying to judge whether a new routine is working, watch the SD as well as the average: a drop in the night-to-night spread is a change in its own right.
Phone battery: how often will it run out?
Suppose you note the battery percentage at bedtime for eight days: 35, 48, 22, 41, 30, 52, 19 and 33. The mean is 35% and the SD is 11.64 points. How worried should you be about dropping below 15% on a normal day? That is (15 − 35) ÷ 11.64 = 1.72 standard deviations below the mean, a z-score of −1.72, and under a normal model it happens on about 4% of days, roughly once a month. None of the eight days in the sample went that low, which fits. Whether that justifies carrying a charger depends on the cost of the bad day, which is a question the SD can size but not answer.
Doing it for your own numbers
The method is the same each time. Write down ten or more ordinary values, work out the mean and SD, and decide how often you can live with being caught out. Mean + 1 SD covers about five days in six, mean + 2 SD about 49 in 50, if the data is roughly bell-shaped. When it is clearly lopsided, sort the values and read off the one at the level you want with the percentile calculator instead. For more on what an SD means, start with what is standard deviation; for examples from work and research, see the use cases page.
Related calculators
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Mean and standard deviation calculator
Paste your own times or bills and get both numbers at once.
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Empirical rule calculator
The 68–95–99.7 bands for any mean and SD.
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Percentile calculator
The data-driven alternative when your numbers are skewed.
Common questions
How many days of data do I need to work out my own standard deviation?
Ten to twenty ordinary days is enough for a useful first estimate of something like a commute or a weekly shop. With fewer than about eight values a single odd day can swing the result a lot. Keep adding days as they come; the estimate settles down as the list grows.
Why is mean + 1 SD about 84% and not 68%?
The 68% figure is for the band from one SD below to one SD above the mean. Planning a departure only cares about one side: you are not late on the fast days. For roughly normal data, 50% of values fall below the mean and another 34% between the mean and one SD above it, so 84% fall below mean + 1 SD.
My commute times are skewed. Can I still use mean + SD?
As a rough guide, yes, but check it against the data. Travel times usually have a long tail of bad days, so the normal percentages can be off. The simplest check is to count: if you want to be on time nine days in ten, sort your times and use the one near the 90th percentile.