Statistics Calculator

Calculated using standard mathematical and industry formulas.

Free online Statistics Calculator calculator and unit conversion tool for everyday, engineering, and home projects.

How to use this calculator?

1. Enter your data values separated by commas or spaces.
2. Read the five-number summary (boxplot inputs), IQR, mean, SD, and skewness all at once.
3. For focused mean/median/mode outputs, use the Mean, Median, Mode Calculator.
4. For standard deviation only, use the Standard Deviation Calculator.

Formula & calculation method

Five-number summary, IQR and skewness

Q1 = 25th percentile · Q3 = 75th percentile · IQR = Q3 − Q1 · Skewness = [N/((N−1)(N−2))] Σ((xᵢ−x̄)/s)³

Percentiles use linear interpolation. Skewness uses the Fisher-Pearson coefficient.

Step-by-step calculation example

[4,8,15,16,23,42,50,60,75]: Q1=11.5, Median=23, Q3=55, IQR=43.5, Mean=32.56, SD=25.1.

Key insights to remember

• The five-number summary (min, Q1, median, Q3, max) is the basis of a boxplot.
• IQR = Q3 − Q1 identifies the middle 50% of data — robust to outliers.
• Outliers can be defined as values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR (Tukey fences).
• Skewness = 0 indicates a symmetric distribution; positive skew means right-heavy; negative means left-heavy.

How to interpret your results?

IQR and outlier detection

Values outside 1.5 × IQR from the quartiles are potential outliers. The IQR is more robust than range for datasets with extreme values.

Skewness

Fisher-Pearson skewness: |skewness| < 0.5 ≈ symmetric, 0.5–1 ≈ moderate skew, > 1 = high skew.

Scope of this calculator

This tool provides a comprehensive summary across all descriptive measures. For a focused analysis of central tendency, use Mean, Median, Mode; for dispersion focus, use Standard Deviation Calculator.

Frequently asked questions

How do I use the Statistics Calculator calculator?

Enter your numerical input and select desired units to get instant accurate results.

How accurate are the conversions?

Conversions use official ISO conversion factors for maximum precision.

Does it convert metric and imperial units?

Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.

Is my data stored?

No, all calculations execute 100% locally in your browser with zero data logging.

Can I use this for DIY or engineering projects?

Yes, it provides reliable estimates for construction, crafting, science, and everyday math.

What if I enter invalid inputs?

The calculator will display a friendly error prompt if non-numeric values are entered.

Related calculators

• Mean, Median, Mode, Range Calculator — Calculate mean (average), median, mode, and range for any dataset — the four pillars of descriptive statistics.
• Standard Deviation Calculator — Calculate sample and population standard deviation, variance, standard error, and coefficient of variation for any dataset.
• Z-score Calculator — Convert a raw score to a Z-score (standard score), find its percentile, and compute cumulative probability under the normal distribution.

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