Standard Deviation Calculator
Calculate the mean, median, standard deviation, and variance for a set of numbers. Supports both population and sample calculations.
This calculator computes descriptive statistics — mean, median, both population and sample standard deviation, both variances, sum, count, and range — from up to ten entered values. Unlike a plain default, an untouched Value 6 through Value 10 field genuinely counts as a real zero in every statistic here: the parsing loop only skips a field when it is undefined or NaN, so a 0 is pushed into the data set exactly like any other number, keeping the default Count at 10 rather than 5. Value 3 has the largest measured effect on Std Deviation (Population) under a small nudge, well ahead of Value 1 or Value 5 — not because it is weighted specially, but because it already sits farthest from the default mean of 7.8 (at 23, versus 10 or 18), and standard deviation's squared-distance formula amplifies a further nudge to whichever value already deviates the most. One consequence of the sensitivity check's own design, not the engine's: Value 6 through Value 10 default to exactly 0, and a percentage-based nudge can never move a value that starts at zero, so none of those five fields can ever appear in a ranked effect list — even though they are counted in every statistic the same as any other entered value.
Inputs
Results
Std Deviation (Population)
8.45
How to Use This Calculator
- Enter up to ten data values in the numbered fields; values set to 0 are treated as actual data points, so only fill in the fields you need.
- Mean (average) is the sum of all values divided by the count of values.
- Variance measures the average squared distance from the mean; Standard Deviation is its square root.
- The calculator reports both population standard deviation (σ, divides by n) and sample standard deviation (s, divides by n−1).
- Use sample standard deviation when your data is a sample from a larger population; use population when you have all the data.
- Range (max − min) and median are also provided for a complete descriptive summary.
How the result changes with Value 3
| Value 3 | Std Deviation (Population) |
|---|---|
| -799,999 | 240,001.53 |
| -300,000 | 90,001.83 |
| 300,000 | 89,998.17 |
| 799,999 | 239,997.87 |
What each input means
- Value 1
- First data point.
- Value 2
- Second data point.
- Value 3
- Third data point.
- Value 4
- Fourth data point.
- Value 5
- Fifth data point.
- Value 6
- Sixth data point.
- Value 7
- Seventh data point.
- Value 8
- Eighth data point.
- Value 9
- Ninth data point.
- Value 10
- Tenth data point.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersValue 1 = 10, Value 2 = 12, Value 3 = 23, Value 4 = 15 = 10 input(s) provided
- Calculate Std Deviation8.4475 = 8.4475
- Calculate Std DeviationStd Deviation8.9044 = 8.9044
- Calculate MeanMean = meanVal7.8 = 7.8
Engine last updated . Checked against 1 independently-derived test — how we verify calculators.
Frequently Asked Questions
If I leave Value 6 through Value 10 blank, are they really counted as zeros?
Yes. The engine's parsing loop only excludes a field when it is undefined or NaN — a value of exactly 0 passes that check and gets pushed into the data set just like any other number. That's why the default Count reads 10, not 5: all five untouched high-numbered fields are treated as genuine zero data points, not as empty slots.
Why does Value 3 move the Std Deviation more than Value 1 does at the default numbers?
Value 3 defaults to 23, the entry farthest from the data set's mean of 7.8, while Value 1 sits much closer at 10. Because standard deviation is built from squared distances to the mean, nudging the entry that's already furthest away amplifies the total more than nudging one that's already close, which is why Value 3 shows the largest measured swing.
Why can't Value 6 through Value 10 ever show up as affecting the result in a sensitivity check?
All five default to exactly 0, and the check works by scaling an input by a fixed percentage of whatever it currently holds — a percentage of zero has nowhere to go. That's a limitation of how the check itself is built, not a sign that those fields don't matter: they are still averaged, squared, and counted like every other entered value.
What's the difference between the Population and Sample standard deviation shown here?
Population standard deviation divides the sum of squared deviations by the full count n, while Sample standard deviation divides by n minus 1 instead — a correction that makes the sample figure slightly larger, intended for use when your data set is a subset of some larger population rather than the entire population itself.
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