What does this calculator do?

Compute statistical results from your inputs.

Enter values in the input fields and view results.

What are the formulas?

See the educational content section for formulas.

For statistical analysis and computation.

Check the related calculators section below.

Results follow standard statistical methods.

4 more

STATISTICSDescriptive StatisticsStatistics Calculator

📊

Descriptive Statistics Calculator

Free descriptive statistics calculator. Mean, median, mode, variance, SD, SEM, CV, skewness, kurtosi

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

📊

STATISTICSDescriptive Statistics

All-in-One Descriptive Stats — Mean, Median, Mode, SD, Skewness, Kurtosis, Quartiles

Comprehensive summary: central tendency, dispersion, shape, and position. Histogram, box plot, step-by-step breakdown.

Standard Deviation →Five Number Summary →

Real-World Scenarios — Click to Load

Data Input

Data — comma or space separated (optional: value,weight per line)

Variance type

descriptive_stats.sh

CALCULATED

$ compute_descriptive --n=85 --type=sample

Count

Mean

72.0000

Median

72.0000

0.0000

Mode

72.0000

Skewness

0.0000

Kurtosis

0.0000

IQR

0.0000

Variance: 0.0000

SEM: 0.0000

MAD: 0.0000

CV: 0.00%

Q1: 72.0000

Q3: 72.0000

Min: 72.0000

Max: 72.0000

Descriptive Statistics Result

All-in-One Summary

Mean = 72.000

Median: 72.00SD: 0.00Skewness: 0.00n = 85

numbervibe.com/calculators/statistics/descriptive-statistics-calculator

Distribution Histogram

Mean: 72.00 | Median: 72.00

Box Plot (5-Number Summary)

Box: Q1–Q3 | Line: Median | Dashed: Mean

Shape: Skewness & Kurtosis vs Normal (0)

Calculation Breakdown

BASIC STATISTICS

Count (n)

Sum (Σx)

6120.0000

Σx = 6120.00

Mean (x̄)

72.0000

x̄ = Σx/n = 6120.00/85

CENTRAL TENDENCY

Median

72.0000

50th ext{percentile}

Mode

72.0000

ext{Most} ext{frequent} ext{value}

RANGE & SPREAD

Min

72.0000

Max

72.0000

Range

0.0000

ext{Max} - ext{Min}

QUARTILES

Q1 (25th)

72.0000

Q2 (50th)

72.0000

Q3 (75th)

72.0000

IQR

0.0000

Q3 - Q1

DISPERSION

Variance (s²)

0.0000

Σ(x−x̄)²/(n−1)

STANDARD DEVIATION (s)

0.0000

√0.0000

SEM

0.0000

SD/√n = 0.0000/√85

MAD

0.0000

ext{Mean} ext{absolute} ext{deviation}

SHAPE

CV (%)

0.00%

( ext{SD}/| ext{mean}|) imes 100

Skewness

0.0000

m_{3}/m_{2}^1.5

Kurtosis

0.0000

m₄/m_{2}^{2} - 3 ( ext{excess})

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

• Central tendency: Mean, median, mode — describe the "center" of your data
• Dispersion: Range, variance, SD, SEM, MAD, CV, IQR — measure spread
• Shape: Skewness (asymmetry), kurtosis (tail heaviness) — describe distribution shape
• Position: Quartiles, percentiles — indicate where values fall relative to the whole
• Population vs sample: Use sample variance (n−1) when estimating from a sample; population when you have the full dataset

Did You Know?

📊The mean is sensitive to outliers; the median is robust. For skewed data, report both.Source: NIST Handbook

📐SEM = SD / √n — measures the precision of the mean estimate, not the spread of data.Source: OpenIntro Statistics

🔍Skewness > 0: right-skewed (long right tail). Skewness < 0: left-skewed.Source: Wolfram MathWorld

📈Kurtosis > 0: heavier tails than normal. Kurtosis < 0: lighter tails.Source: Rice Virtual Lab

🧪Geometric mean is used for growth rates; harmonic mean for rates (e.g., average speed).Source: Khan Academy

📉MAD (median absolute deviation) is robust to outliers, unlike SD.Source: Penn State STAT 500

How It Works

1. Central Tendency

Mean = sum/n. Median = 50th percentile. Mode = most frequent value.

2. Dispersion

Variance = Σ(x−μ)²/(n−1) for sample. SD = √variance. SEM = SD/√n.

3. Shape

Skewness = m₃/m₂^1.5. Kurtosis = m₄/m₂² − 3 (excess kurtosis).

4. Quartiles & Percentiles

Linear interpolation between adjacent values. Q1 = P25, Q2 = P50 (median), Q3 = P75.

5. Population vs Sample

Sample variance uses n−1 (Bessel correction). Population uses n.

Expert Tips

Report Both Mean and Median

If they differ significantly, your data is skewed. Report both for transparency.

Use SEM for Inference

When reporting mean ± error, use SEM. For spread of data, use SD.

Check Normality

Q-Q plot and skewness/kurtosis help. Many parametric tests assume normality.

Weighted Data

Use value,weight format per line for weighted mean. Default: equal weights.

Why Use This Calculator vs. Other Tools?

Feature	This Calculator	Excel	R
All stats in one place	✅	⚠️ Multiple functions	✅ summary()
Skewness & kurtosis	✅	⚠️ SKEW, KURT	✅ moments
Histogram + box plot	✅	⚠️ Manual	✅
Population vs sample	✅	⚠️	✅
Copy & share results	✅	❌	❌
AI-powered interpretation	✅	❌	❌

Frequently Asked Questions

When to use mean vs median?

Mean for symmetric data. Median for skewed data or when outliers are present. Report both when in doubt.

What is SEM?

Standard error of the mean = SD/√n. Measures how precisely the sample mean estimates the population mean.

What does skewness mean?

Skewness > 0: right tail longer. Skewness < 0: left tail longer. Skewness ≈ 0: symmetric.

What is excess kurtosis?

Kurtosis − 3. Normal distribution has excess kurtosis 0. Positive: heavy tails. Negative: light tails.

Population vs sample variance?

Sample: divide by n−1 (unbiased estimator). Population: divide by n. Use sample when you have a subset.

What is MAD?

Median absolute deviation — median of |x − median|. Robust to outliers.

What is CV?

Coefficient of variation = (SD/mean)×100%. Allows comparing variability across different scales.

Formulas Reference

Mean: μ = Σx/n

Variance (sample): s² = Σ(x−μ)²/(n−1)

SEM = s/√n

CV = (s/mean)×100%

Skewness = m₃/m₂^1.5, Kurtosis = m₄/m₂² − 3

IQR = Q3 − Q1

Descriptive Stats by the Numbers

68%

Within ±1 SD (normal)

95%

Within ±2 SD (normal)

Skewness for symmetric

Excess kurtosis (normal)

Official Data Sources

NIST Engineering Statistics Handbook ↗

Definitive reference for statistical methods

Updated: 2024

Penn State STAT 500 ↗

University-level descriptive statistics

Updated: 2025

OpenIntro Statistics ↗

Free open-source statistics textbook (4th ed.)

Updated: 2024

Khan Academy - Descriptive Statistics ↗

Interactive lessons on mean, median, SD

Updated: 2025

Rice Virtual Lab in Statistics ↗

Simulations and applets for data analysis

Updated: 2024

Wolfram MathWorld ↗

Mean, variance, skewness definitions

Updated: 2025

Hyndman & Fan (1996) ↗

Sample quantile definitions

Updated: 1996

Disclaimer: Population vs sample variance affects SD and variance. Use sample when estimating from a subset; population when you have full data. This tool is for educational and professional reference purposes.

👈 START HERE

⬅️Jump in and explore the concept!

Descriptive Statistics Calculator

Why This Statistical Analysis Matters

All-in-One Descriptive Stats — Mean, Median, Mode, SD, Skewness, Kurtosis, Quartiles

Real-World Scenarios — Click to Load

Data Input

Distribution Histogram

Box Plot (5-Number Summary)

Shape: Skewness & Kurtosis vs Normal (0)

Calculation Breakdown

Key Takeaways

Did You Know?

How It Works

1. Central Tendency

2. Dispersion

3. Shape

4. Quartiles & Percentiles

5. Population vs Sample

Expert Tips

Report Both Mean and Median

Use SEM for Inference

Check Normality

Weighted Data

Why Use This Calculator vs. Other Tools?

Frequently Asked Questions

When to use mean vs median?

What is SEM?

What does skewness mean?

What is excess kurtosis?

Population vs sample variance?

What is MAD?

What is CV?

Formulas Reference

Descriptive Stats by the Numbers

Official Data Sources

Related Statistics Calculators

Related Calculators

Dot Plot Calculator

Percentile Calculator

Dispersion Calculator

Five Number Summary Calculator

Box Plot Calculator

IQR Calculator (Interquartile Range)

We Value Your Privacy