⚗

FREETOOLS LABS

Mathematics

Statistics Calculator

Analyze number series, weighted data, correlations and linear regression in one tool.

Analyze data

Separate numbers with spaces, line breaks or semicolons. Decimal commas and points are supported.

Result

Overview

5

Overview

Count n8
Sum40
Median4.5
Mode4
Minimum2
Maximum9
Range7

Dispersion

Population variance σ²4
Population standard deviation σ2
Sample variance s²4.57142857143
Sample standard deviation s2.1380899353
Mean absolute deviation1.5
Median absolute deviation0.5
Standard error (SEM)0.755928946018
Population coefficient of variation40 %
Sample coefficient of variation42.761798706 %

Distribution

Q14
Median4.5
Q35.5
Interquartile range1.5
P907.6
Tukey fences1.75 – 7.75
Potential outliers9

Additional measures

Geometric mean4.60321559605
Harmonic mean4.20175072947
Root mean square (RMS)5.38516480713
Sum of squares232
Sum of squared deviations32

Histogram (Sturges rule)

Box plot with Tukey outliers

Frequency table

ValueAbsolute frequencyRelative frequencyCumulativeCumulative relative
2112.5 %112.5 %
4337.5 %450 %
5225 %675 %
7112.5 %787.5 %
9112.5 %8100 %

Deviation table

Valuex − mean(x − mean)²Z-score
2-39-1.5
4-11-0.5
4-11-0.5
4-11-0.5
5000
5000
7241
94162

Statistical methods

Mean, median and mode describe location; variance and standard deviation describe dispersion. Population divides by n, sample variance by n − 1.

Quartiles and custom percentiles use Type 7: h = (n − 1) × p with linear interpolation. Tukey fences identify potential outliers only.

Pearson measures linear association; Spearman measures monotonic rank association using average ranks for ties. Correlation does not prove causation.

Frequently asked questions

Which standard deviation should I use?

Use σ for the entire population and usually s for a sample. Both are shown.

Why can quartiles differ?

Several conventions exist. This calculator consistently uses Type 7.

What does R² mean?

In linear regression, R² is the share of variation in Y explained by the model.

How does a weighted mean work?

Each value contributes according to its weight.