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Analysis · Probability

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.

Summarizing Data Without Fooling Yourself

The measures and what each one hides

Every summary statistic compresses — knowing what each discards is the skill:

Measure	Tells you	Hides / breaks when
Mean	The balance point	One billionaire walks into the room
Median	The middle person	Robust to outliers — use for incomes, prices
Mode	The most common value	Useless on continuous data
Range	Total spread	Driven entirely by the two extremes
Standard deviation	Typical distance from mean	Misleading on skewed data

Mean vs median is a worldview choice

Average salary at a company of nine modest earners and one director: the mean flatters, the median tells the truth. Property prices, household incomes, response times — anything skewed — reports more honestly as a median. When mean and median diverge sharply, that gap itself is information: the distribution has a tail, and whoever quotes only the mean may be selling something.

Beyond the summary

Spread gets its own deep-dive in the standard deviation calculator (with steps for coursework), chance questions about the data belong to the probability calculator, and percentage changes between two summaries compute in the percentage calculator.