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Descriptive Statistics Calculator

Calculate comprehensive descriptive statistics including mean, median, mode, standard deviation, and variance with our free online tool.

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Measures of Central Tendency

Calculate mean, median, and mode with our comprehensive central tendency calculator. Includes weighted averages, trimmed means, and geometric means for specialized analysis needs.

  • Arithmetic mean calculator
  • Median finder with interpolation
  • Mode detection (unimodal/multimodal)
  • Weighted average calculator
  • Geometric and harmonic means

Measures of Dispersion

Comprehensive variance and standard deviation calculator with population and sample statistics. Includes range, interquartile range, and coefficient of variation for complete data spread analysis.

  • Standard deviation (sample & population)
  • Variance calculator
  • Interquartile range (IQR)
  • Range and coefficient of variation
  • Mean absolute deviation

Data Visualization Tools

Generate histograms, box plots, and summary charts automatically. Visual data exploration with outlier detection and distribution shape analysis for comprehensive statistical understanding.

  • Histogram generator
  • Box plot creator
  • Stem-and-leaf plots
  • Outlier detection and highlighting
  • Distribution shape analysis

Understanding Descriptive Statistics Measures

Mean (Average)

Sum of all values divided by count. Best for normally distributed data without extreme outliers. Sensitive to extreme values.

Median (Middle Value)

Middle value when data is ordered. Robust against outliers, ideal for skewed distributions. 50th percentile of the dataset.

Mode (Most Frequent)

Most frequently occurring value. Useful for categorical data and identifying peaks in distributions. Can be unimodal or multimodal.

Standard Deviation

Square root of variance, measures spread in original units. Approximately 68% of data falls within 1 SD of mean in normal distributions.

Descriptive Statistics: When to Use Each Measure

Data Type Best Central Tendency Best Dispersion Measure Use Case
Normal Distribution Mean Standard Deviation Most statistical tests, parametric analysis
Skewed Distribution Median Interquartile Range (IQR) Income data, reaction times, non-parametric tests
Categorical Data Mode Frequency Distribution Survey responses, preferences, classifications
Data with Outliers Median or Trimmed Mean IQR or MAD Robust analysis, exploratory data analysis

Frequently Asked Questions

What is the difference between standard deviation and variance?
Variance is the average of squared differences from the mean, while standard deviation is the square root of variance. Standard deviation is in the same units as your data, making it easier to interpret. Both measure data spread, but standard deviation is more commonly used for interpretation.
When to use median instead of mean?
Use median when data is skewed or contains outliers, as it's less affected by extreme values. Use mean for normally distributed data. Median is the middle value when data is ordered, while mean is the arithmetic average. For income data, house prices, or reaction times, median is often more representative.
How to calculate descriptive statistics for grouped data?
For grouped data, use class midpoints and frequencies. Mean = Σ(midpoint × frequency) / total frequency. Use interpolation for median and mode. Our calculator handles both raw and grouped data automatically, providing accurate results for frequency tables and class intervals.
What is the five number summary?
The five number summary includes minimum, Q1 (25th percentile), median (Q2), Q3 (75th percentile), and maximum. It provides a complete picture of data distribution and is used to create box plots. This summary is particularly useful for identifying outliers and understanding data spread.

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