Statistics Calculator

Mean, median, mode, std dev & more

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About Statistics Calculator

A comprehensive descriptive statistics calculator. Enter a dataset and instantly compute mean, median, mode, range, variance, standard deviation (population and sample), quartiles (Q1, Q2, Q3), interquartile range, skewness, and kurtosis. Shows step-by-step calculations for each statistic, sorted data, frequency distribution, and a five-number summary. All computation runs client-side. Essential for students, researchers, data analysts, and anyone performing statistical analysis.

Statistics Calculator Features

  • Mean/median/mode
  • Std deviation
  • Quartiles & IQR
  • Step-by-step
  • Five-number summary
Descriptive statistics summarize datasets with a few key numbers. The mean tells you the average, the median tells you the middle value, and the standard deviation tells you how spread out the data is. This calculator computes all major descriptive statistics with step-by-step explanations.

How to Use

Enter your data as comma-separated numbers:

  • Central tendency: Mean, median, mode
  • Spread: Range, variance, standard deviation
  • Position: Quartiles, percentiles, IQR

Key Formulas

  • Mean: Sum of all values / count
  • Variance: Average of squared deviations from mean
  • Std Dev: Square root of variance
  • Sample vs Population: Sample divides by n-1 (Bessel's correction)

Interpreting Results

Low std dev means data points cluster near the mean. High std dev means they're spread out. The IQR (Q3-Q1) contains the middle 50% of data. Skewness measures asymmetry (0 = symmetric).

Step-by-Step Instructions

  1. 1Enter numbers separated by commas.
  2. 2View central tendency measures (mean, median, mode).
  3. 3Check spread measures (range, variance, std dev).
  4. 4Review quartiles and five-number summary.
  5. 5Study the step-by-step calculations.

Statistics Calculator — Frequently Asked Questions

When should I use mean vs median?+

Use the mean for symmetric distributions. Use the median when data has outliers or is skewed — the median is resistant to extreme values. For example, median household income is more informative than mean income because a few billionaires skew the mean.

What's the difference between population and sample standard deviation?+

Population std dev (σ) divides by N. Sample std dev (s) divides by N-1 (Bessel's correction) to provide an unbiased estimate of the population parameter. Use sample when your data is a subset of a larger population.

What does the interquartile range tell me?+

The IQR (Q3-Q1) spans the middle 50% of data. It's a robust measure of spread because it's not affected by outliers. Values beyond Q1-1.5×IQR or Q3+1.5×IQR are often considered outliers.

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