Statistics Calculator

Calculate standard deviation, variance, mean, median, skewness, IQR percentiles, detect outliers, and render dynamic SVG Box Plots.

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Dataset Input

Sample:··

Methodology

Count (n)

Sum (Σ)

473

Mean (μ)

31.5333

Median

Mode

No Mode

Range

Variance (σ²)

212.9156

Std. Dev (σ)

14.5916

Coeff. of Variation

46.27%

Box & Whisker Visualization

Min: 12Q1: 20.5Median: 29.0Q3: 39.5Max: 68

Deviation Analysis

Value	Deviation (x-μ)	Squared Dev	Z-Score
24	-7.5333	56.7511	-0.52
15	-16.5333	273.3511	-1.13
38	+6.4667	41.8178	+0.44
45	+13.4667	181.3511	+0.92
12	-19.5333	381.5511	-1.34
68	+36.4667	1329.8178	+2.50
22	-9.5333	90.8844	-0.65
19	-12.5333	157.0844	-0.86
31	-0.5333	0.2844	-0.04
27	-4.5333	20.5511	-0.31
41	+9.4667	89.6178	+0.65
18	-13.5333	183.1511	-0.93
29	-2.5333	6.4178	-0.17
33	+1.4667	2.1511	+0.10
51	+19.4667	378.9511	+1.33

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Statistics Mathematical Formulas

Theoretical definitions of calculation methods.

Mean (Average)

x̄ = ( Σ x_i ) / n

The sum of all dataset elements divided by total observations count.

Variance

σ² = Σ(x_i - μ)² / N

Measures how far each dataset number is spread from the mean.

Std. Deviation

σ = √[ Σ(x_i - μ)² / N ]

Square root of variance; indicates standard dispersion of elements.

Z-Score

z = (x - μ) / σ

Represents standard deviations count a single point is away from mean.

Frequently Asked Questions

What is the difference between Population and Sample statistics?

Population statistics evaluate the entire population, while sample statistics represent a small subset. The core calculation difference lies in variance: population divides the squared deviations by n, whereas sample dividing divides by n - 1 (Bessel's correction) to correct bias.

How are outliers calculated?

We use the standard IQR (Interquartile Range) method. We compute boundaries (fences) at Q1 - 1.5×IQR and Q3 + 1.5×IQR. Any point outside these ranges is classified as a statistical outlier.

Can I export deviation data?

Yes, you can copy sorted lists or deviation tables directly from our high-density analytical dashboard into excel or spreadsheets.