Kalkulator deviasi standar
The detailed guide below is currently available in English.
Sample versus population standard deviation
Both versions measure how far your numbers typically sit from their mean, but they divide the squared deviations by different counts. The sample standard deviation s divides by n − 1, which corrects for the fact that a sample underestimates spread; the population standard deviation σ divides by n and is used when your data is the entire group. The two agree more closely as the count grows, and with a small list the difference can be noticeable.
The other numbers in the results
The mean is the arithmetic average: add everything, divide by the count. The median is the middle value once the list is sorted (the average of the two middle values for an even count) and is less swayed by outliers. The variance is the squared standard deviation, useful in its own right in probability work. The minimum, maximum, and range describe the span of the data at a glance, which makes them a quick sanity check on typos before you trust the spread numbers.
Pertanyaan umum
When should I use sample σ instead of population σ?
Use the sample value when your numbers are a subset of something larger — ten test wells out of an aquifer, a poll of voters out of a country. Use the population value only when the list really is everything you care about, such as all five machines in a workshop.
Why does the formula divide by n − 1?
A sample tends to sit slightly closer to its own mean than to the true population mean, so its squared deviations come out too small. Dividing by n − 1 instead of n, called Bessel’s correction, inflates the result just enough to remove that bias on average.
How do I enter the data?
Type or paste the numbers in any order, separated by commas, spaces, or semicolons — the calculator splits on all three, so spreadsheet column pastes usually work as-is. Negative numbers and decimals are welcome; anything that is not a number is flagged so you can fix it.