The calculation, without hidden assumptions
A useful descriptive-statistics calculator should summarize location, spread and distribution without forcing the same dataset through a dozen separate pages. MAXScanner accepts pasted values from a spreadsheet, supports value:frequency shorthand, reports the main center and spread measures together, keeps sample and population variance/standard deviation visible, and states the quartile convention used. It also shows a frequency table and Tukey outlier fences so repeated values and possible extremes are not hidden behind one average.
How to use this calculator
Paste numbers separated by commas, spaces, semicolons or new lines; a spreadsheet column can be pasted directly, and value:frequency shorthand can expand repeated observations.
Choose Sample when the observations are a subset used to estimate a larger population, or Population when the dataset contains every observation you mean to describe.
Read the center, spread, quartiles and outlier outputs together, then use the frequency table and sorted-data line to inspect the distribution rather than relying on the mean alone.
Where people use it
- •Summarizing survey, test, laboratory or operational measurements
- •Comparing mean, median and mode on skewed or repeated datasets
- •Checking quartiles, IQR and Tukey outlier candidates
- •Getting sample and population variance/standard deviation from the same data
Example: 2, 4, 4, 4, 5, 5, 7, 9
This classic dataset has mean 5 and population variance 4, so the population standard deviation is 2. Using the sample denominator n−1 gives variance about 4.5714 and sample standard deviation about 2.1381. The same input also exposes the median, mode, quartiles, IQR and frequency counts.
What the result does not assume
- •Quartiles and percentiles have multiple accepted calculation conventions. MAXScanner uses the Tukey median-of-halves method: for odd-sized datasets the overall median is excluded from the lower and upper halves. Other software can legitimately return different Q1/Q3 values when it uses interpolation.
- •Tukey fences flag observations outside Q1−1.5×IQR or Q3+1.5×IQR as candidates for inspection; they do not prove that a value is erroneous and should not be deleted automatically.
- •Moment skewness and excess kurtosis are descriptive population-moment measures here. Small samples can make shape statistics unstable, so interpret them with the dataset context.
Frequently asked questions
What is the difference between sample and population standard deviation?+
Population SD divides the squared-deviation sum by N because the dataset is the whole population being described. Sample SD divides by n−1 when the data are a sample used to estimate variability in a larger population.
How are Q1 and Q3 calculated?+
MAXScanner sorts the values and uses the Tukey median-of-halves method. With an odd count, it excludes the overall median before finding the lower-half and upper-half medians.
Can a dataset have more than one mode?+
Yes. If several values tie for the highest repeated frequency, all of them are reported. If every value occurs once, the calculator reports no repeated mode.
Can I paste data from Excel or Google Sheets?+
Yes. Commas, spaces, semicolons and new lines are accepted. A one-column spreadsheet selection normally pastes as new-line-separated values.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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Keep the result connected to the real job
MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.