Descriptive Statistics Calculator

Calculate comprehensive descriptive statistics including central tendency, dispersion, and distribution shape

Calculate Descriptive Statistics

Sample data represents a subset; population data represents the entire group

You can enter up to 1000 values. At least 2 values are required for meaningful statistics.

What are Descriptive Statistics?

Summarize and describe key features of datasets

Measure central tendency (mean, median, mode)

Assess variability and dispersion

Identify outliers and distribution shape

Provide foundation for inferential statistics

Key Statistical Measures

Central Tendency

Mean, median, mode, midrange

Dispersion

Variance, standard deviation, range, IQR

Position

Quartiles, percentiles, five-number summary

Shape

Skewness, kurtosis

Outliers

Fences, outlier identification

Sample vs Population

Sample Data

Subset of the population

Uses n-1 for variance calculation (Bessel's correction)

Population Data

Complete dataset

Uses n for variance calculation

Tip: Use "Sample" for most real-world data analysis scenarios

Understanding Descriptive Statistics

What are Descriptive Statistics?

Descriptive statistics are numerical summaries that describe the main features of a dataset. They provide simple summaries about the sample and the measures, forming the basis of virtually every quantitative analysis of data.

Categories of Descriptive Statistics

  • Central Tendency: Where the data clusters (mean, median, mode)
  • Variability: How spread out the data is (variance, standard deviation)
  • Distribution: The shape of the data (skewness, kurtosis)

Interpretation Guidelines

Skewness Interpretation

  • |Skew| < 0.5: Approximately symmetric
  • Skew > 0.5: Positively skewed (right tail)
  • Skew < -0.5: Negatively skewed (left tail)

Kurtosis Interpretation

  • |Kurt| < 0.5: Mesokurtic (normal-like)
  • Kurt > 0.5: Leptokurtic (heavy tails)
  • Kurt < -0.5: Platykurtic (light tails)

Practical Applications

Quality Control

Monitor process variation and identify out-of-control conditions

Market Research

Understand customer behavior patterns and preferences

Academic Assessment

Analyze test scores and grade distributions