what does this symbol mean?

Statistics symbols

The symbols of statistics, from x̄ and p̂ to r, R² and H₀, what each one stands for and how to tell the sample from the population.

Describing data 5 symbols

Relationships 3 symbols

Testing 2 symbols

About statistics symbols

Statistics symbols mostly come in pairs. A number that describes a whole population is a parameter, and a number calculated from a sample to estimate it is a statistic, in the definitions of OpenStax’s Introductory Statistics. The usual habit is to write the parameter with a Greek letter and the statistic with a Latin one, or with a bar or a hat. Each page here says what one symbol stands for, how it is read, how it differs from its partner and where the notation came from. The readings are from OpenStax’s free textbook, published by Rice University, Penn State’s online statistics courses and NIST’s Engineering Statistics Handbook; the histories are from Jeff Miller’s Earliest Uses of Symbols in Probability and Statistics, published by the University of St Andrews.

Sample and population

QuantitySample (statistic)Population (parameter)
Meanx̄μ
Standard deviationsσ
Variances²σ²
Proportionp̂p
Correlationrρ
SizenN

The Greek letters have their own pages in Greek letters, which give their other jobs in science. Not every row follows the rule. Penn State’s notes write the population proportion with a Latin p, so for a proportion only the hat tells the sample from the population, and NIST’s handbook writes N for the number of values in a sample.

Bars and hats

A bar means a mean: x̄ is read “x bar”. A hat means an estimate: p̂ is read “p hat”, and ŷ, “y hat”, is the value of y a regression line predicts. Miller calls the bar a relic of a convention that has otherwise vanished, from applied mathematicians who marked any kind of average with one, and dates the hat for estimates to the 1920s and 1930s.

Regression and testing

R², the coefficient of determination, is the share of the variation in y that a regression accounts for. H₀ is the null hypothesis, tested against an alternative written Hₐ or H₁, and the p-value measures the evidence against it. The significance level a p-value is compared with is the Greek α, and the chi-square distribution is written with another Greek letter, χ².

Where the notation came from

Miller writes that none of the notation used by Laplace and Gauss survived into modern statistics. The oldest still in use dates from 1890 to 1940, when the British statisticians Karl Pearson and R. A. Fisher introduced many of the basic symbols. Pearson first wrote σ for the standard deviation in 1894; Francis Galton had chosen r for correlation in 1888; and Fisher’s insistence on separating parameters from estimates produced the Greek and Latin pairs.

Sources

  1. Introductory Statistics 2e, 1.1 Definitions of Statistics, Probability, and Key Terms, OpenStax (Rice University), Section 1.1, Key Terms
  2. Introductory Statistics 2e, 2.5 Measures of the Center of the Data, OpenStax (Rice University), Section 2.5
  3. Introductory Statistics 2e, 2.7 Measures of the Spread of the Data, OpenStax (Rice University), Section 2.7, Standard deviation; Example 2.32; Figure (TI calculator screen)
  4. Introductory Statistics 2e, 8.3 A Population Proportion, OpenStax (Rice University), Section 8.3
  5. Introductory Statistics 2e, 9.1 Null and Alternative Hypotheses, OpenStax (Rice University), Section 9.1; Table 9.1; Examples 9.2 and 9.4
  6. Introductory Statistics 2e, 9.4 Rare Events, the Sample, and the Decision and Conclusion, OpenStax (Rice University), Section 9.4
  7. Introductory Statistics 2e, 12.3 The Regression Equation, OpenStax (Rice University), Section 12.3; The Correlation Coefficient r; The Coefficient of Determination
  8. Introductory Statistics 2e, 11.1 Facts About the Chi-Square Distribution, OpenStax (Rice University), Section 11.1
  9. Introductory Statistics 2e, 12.4 Testing the Significance of the Correlation Coefficient, OpenStax (Rice University), Section 12.4
  10. STAT 500 Applied Statistics, 0.2 Foundations, Penn State online course notes (archived copy), Penn State Eberly College of Science, Department of Statistics, Populations and Parameters; Samples and Statistics
  11. STAT 500 Applied Statistics, 6a.1 Introduction to Hypothesis Testing, Penn State online course notes (archived copy), Penn State Eberly College of Science, Department of Statistics, Null hypothesis; Alternative hypothesis
  12. STAT 500 Applied Statistics, 1.5.1 Measures of Central Tendency, Penn State online course notes (archived copy), Penn State Eberly College of Science, Department of Statistics, Mean
  13. 1.3.5.1. Measures of Location, NIST/SEMATECH e-Handbook of Statistical Methods, National Institute of Standards and Technology (NIST), Definition of Location
  14. Earliest Uses of Symbols in Probability and Statistics, Jeff Miller, Earliest Uses of Various Mathematical Symbols, MacTutor History of Mathematics, University of St Andrews, Symbols in Statistics; Symbols associated with the normal distribution; Symbols associated with testing hypotheses

Last reviewed October 8, 2026 by Rory Hansen. How we research