Symbol Sheet / SWT

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Updated 5 Nov 2020 (What’s New?) Copyright © 2002–2025 by Stan Brown, BrownMath.com

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Relational Symbols
=	equalsis the same as	≠	is not equal tois different from
>	is greater thanis more thanexceedsis above	≥or >=	is greater than or equal tois at leastis not less than
<	is less thanis fewer thanis below	≤or <=	is less than or equal tois at mostdoes not exceedis not greater thanis no more than
A < x < B		x is between A and B, exclusive
A ≤ x ≤ B		x is between A and B, inclusive
A ≈ B		A is approximately equal to B

Here are symbols for various sample statistics and the corresponding population parameters. They are not repeated in the list below.

samplestatistic	populationparameter	description
n	N	number of members of sample or population
x̅ “x-bar”	μ “mu”or μx	mean
M or Medor x̃ “x-tilde”	(none)	median
s (TIs say Sx)	σ “sigma” or σx	standard deviationFor variance, apply a squared symbol (s² or σ²).
r	ρ “rho”	coefficient of linear correlation
p̂ “p-hat”	p	proportion
z t χ²	(n/a)	calculated test statistic

μ and σ can take subscripts to show what you are taking the mean or standard deviation of. For instance, σx̅ (“sigma sub x-bar”) is the standard deviation of sample means, or standard error of the mean.

Roman Letters

• b = y intercept of a line. Defined here in Chapter 4. (Some statistics books use b0.)
• BD or BPD = binomial probability distribution. Defined here in Chapter 6.
• CI = confidence interval. Defined here in Chapter 9.
• CLT = Central Limit Theorem. Defined here in Chapter 8.
• d = difference between paired data. Defined here in Chapter 11.
• df or ν “nu” = degrees of freedom in a Student’s t or χ² distribution. Defined here in Chapter 9. Defined here in Chapter 12.
• DPD = discrete probability distribution. Defined here in Chapter 6.
• E = margin of error, a/k/a maximum error of the estimate. Defined here in Chapter 9.
• f = frequency. Defined here in Chapter 2.
• f/n = relative frequency. Defined here in Chapter 2.
• HT = hypothesis test. Defined here in Chapter 10.
• Ho = null hypothesis. Defined here in Chapter 10.
• H1 or Ha = alternative hypothesis. Defined here in Chapter 10.
• IQR = interquartile range, Q3−Q1. Defined here in Chapter 3.
• m = slope of a line. Defined here in Chapter 4. (The TI-83 uses a and some statistics books use b1.)
• M or Med = median of a sample. Defined here in Chapter 3.
• n = sample size, number of data points. Defined here in Chapter 2. Also, number of trials in a probability experiment with a binomial model. Defined here in Chapter 6.
• N = population size.
• ND = normal distribution, whose graph is a bell-shaped curve; also “normally distributed”. Defined here in Chapter 7.
• p = probability value. The specific meaning depends on context.

  In geometric and binomial probability distributions, p is the probability of “success” (defined here in Chapter 6) on any one trial and q = (1−p) is the probability of “failure” (the only other possibility) on any one trial.

  In hypothesis testing, p is the calculated p-value (defined here in Chapter 10), the probability that rejecting the null hypothesis would be a wrong decision.

  In tests of population proportions, p stands for population proportion and p̂ for sample proportion (see table above).

• P(A) = the probability of event A.
• P(AC) or P(not A) = the probability that A does not happen. Defined here in Chapter 5.
• P(B | A) = the probability that event B will happen, given that event A definitely happens. It’s usually read as the probability of B given A. Defined here in Chapter 5.

  Caution! The order of A and B may seem backward to you at first.

• P80 or P80 = 80th percentile (Pk or Pk = k-th percentile) Defined here in Chapter 3.
• q = probability of failure on any one trial in binomial or geometric distribution, equal to (1−p) where p is the probability of success on any one trial. Defined here in Chapter 6.
• Q1 or Q1 = first quartile (Q3 or Q3 = third quartile) Defined here in Chapter 3.
• r = linear correlation coefficient of a sample. Defined here in Chapter 4.
• R² = coefficient of determination. Defined here in Chapter 4.
• s = standard deviation of a sample. Defined here in Chapter 3.
• SD (or s.d.) = standard deviation. Defined here in Chapter 3.
• SEM = standard error of the mean (symbol is σx̅). Defined here in Chapter 8.
• SEP = standard error of the proportion (symbol is σp̂). Defined here in Chapter 8.
• X (capital X) = a variable.
• x (lower-case x) = one data value (“raw score”). As a column heading, x means a series of data values.
• x̅ “x-bar” = mean of a sample. Defined here in Chapter 3.
• x̃ “x-tilde” = median of a sample. Defined here in Chapter 3.
• ŷ “y-hat” = predicted average y value for a given x, found by using the regression equation. Defined here in Chapter 4.
• z = standard score or z-score. Defined here in Chapter 3.
• z(area) or zarea = the z-score, such that that much of the area under the normal curve lies to the right of that z. This is not a multiplication! (See The z Function.)

Greek Letters

• α “alpha” = significance level in hypothesis test, or acceptable probability of a Type I error (probability you can live with). Defined here in Chapter 10. 1−α = confidence level.
• β “beta” = in a hypothesis test, the acceptable probability of a Type II error; 1−β is called the power of the test.
• μ mu, pronounced “mew” = mean of a population. Defined here in Chapter 3.
• ν nu: see df, above.
• ρ rho, pronounced “roe” = linear correlation coefficient of a population.
• σ “sigma” = standard deviation of a population. Defined here in Chapter 3.
• σx̅ “sigma-sub-x-bar”; see SEM above.
• σp̂ “sigma-sub-p-hat”; see SEP above.
• ∑ “sigma” = summation. (This is upper-case sigma. Lower-case sigma, σ, means standard deviation of a population; see the table near the start of this page.) See ∑ Means Add ’em Up in Chapter 1.
• χ² “chi-squared” = distribution for multinomial experiments and contingency tables. Defined here in Chapter 12.

What’s New?

• 5 Nov 2020: Convert document to HTML5, and italicize the variables.
• 14 Feb 2018: Add x̃ for the median, as suggested by reader “Trone”.
• (intervening changes suppressed)
• 27 Sept 2002: New article.

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