Statistics Calculator
Calculate statistical measures. Standard deviation, variance, quartiles and more. Online calculator with solution path and worked examples.
Result
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Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
What is standard deviation?
Standard deviation measures how spread out values are from the mean. A low standard deviation means values cluster near the mean. A high one means they are more spread out.
What is the difference between population and sample statistics?
Population statistics describe the entire group. Sample statistics describe a subset and include corrections (like using n-1 in variance) to estimate population parameters from the sample.
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
Quick Answer
The statistics calculator computes statistical measures: mean, standard deviation, variance, median, quartiles and range.
What is the Statistics Calculator?
The statistics calculator computes statistical measures: mean, standard deviation, variance, median, quartiles and range.
How does the Statistics Calculator work?
Enter your data series. The calculator determines all common descriptive statistics: location parameters (mean, median, quartiles) and dispersion parameters (variance, standard deviation, range, interquartile range).
Key Data and Facts
Standard deviation = square root of variance. 68-95-99.7 rule for normal distributions: 68% of values lie within +/- 1 standard deviation of the mean.
Step-by-Step Guide
How to use the statistics calculator step by step: 1. Enter the data series -- enter your numerical values, separated by a comma or semicolon, e.g. exam results or measured values. 2. Read off the measures of location -- the mean (arithmetic mean) shows the average, the median the middle value of the sorted data. With skewed distributions the two diverge. 3. Check the measures of dispersion -- the standard deviation shows how strongly the values spread around the mean. Small values mean homogeneous data, large values strong dispersion. 4. Look at the quartiles and the range -- Q1 (25 %) and Q3 (75 %) bound the middle 50 % of the data. The interquartile range (IQR = Q3 - Q1) is robust against outliers. 5. Interpret the results: if the values are normally distributed, about 68 % lie within +/- 1 standard deviation. Compare the key figures to identify trends or outliers.
Calculation Example
Datenreihe: 4, 7, 8, 9, 12. Mittelwert: (4+7+8+9+12)/5 = 8,0. Median: 8. Varianz: 6,8. Standardabweichung: 2,61.
Sources · E-E-A-T
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Mathematics
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