TC3 → Stan Brown → Statistics → Symbols
revised 18 Sep 2012

# Symbol Sheetfor MATH200 (Statistics)

Relational Symbols
=   equals
is the same as
is not equal to
is different from
>   is greater than
is more than
exceeds
is above

or >=
is greater than or equal to
is at least
is not less than
<   is less than
is fewer than
is below

or <=
is less than or equal to
is at most
does not exceed
is not greater than
is 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.

sample
statistic
population
parameter
description
“x-bar” μ “mu”
or μx
mean
M
(TIs say Med)
(none) median
s
(TIs say Sx)
σ “sigma”
or σx
standard deviation
For variance, apply a squared symbol (s² or σ²).
r ρ “rho” coefficient of linear correlation
“p-hat” p proportion
zo   to   χ²o (n/a) calculated test statistic

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

Other symbols — Roman letters

• b = y intercept of a line (Some statistics books use b0.)
• BD or BPD = binomial probability distribution
• CLT = Central Limit Theorem
• d = difference between paired data
• df or ν “nu” = degrees of freedom in a Student’s t or χ² distribution
• DPD = discrete probability distribution
• E = margin of error, a/k/a maximum error of the estimate
• f = frequency
• f/n = relative frequency
• Ho = null hypothesis
• H1 or Ha = alternative hypothesis
• IQR = interquartile range, Q3−Q1
• m = slope of a line (The TI-83 uses a and some statistics books use b1.)
• n = sample size, number of data points, or number of trials in a probability experiment
• ND = normal distribution, whose graph is a bell-shaped curve; also “normally distributed”
• p = probability value. In binomial probability distributions p is the probability of “success” (however defined) 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, the probability that rejecting the null hypothesis would be a wrong decision. In tests of population proportions, p stands for population proportion and for sample proportion (see table above). You have to rely on context to know what “p” means.

• P(A) = the probability of event A. (Sometimes P′(A) is used to distinguish the experimental probability of event A from the theoretical probability.)
• P(AC) = probability of not-A, the probability that A does not happen
• P80 or P80 = 80th percentile (Pk or Pk = k-th percentile)
• Q1 or Q1 = first quartile (Q3 or Q3 = third quartile)
• = coefficient of determination
• SEM = standard error of the mean (symbol is σ)
• SEP = standard error of the proportion (symbol is σ)
• x = a variable or a data value (raw score). As a column heading, x means a series of data values.
• ŷ “y-hat” = predicted average y value for a given x, found by using the regression equation
• z = standard score or z-score. Using the individual score x, the mean μ, and the standard deviation σ, the formula is
Using a sample mean and comparing it to the distribution of sample means, the formula is
• 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 Normal Calculations on TI-83/84 or TI-89.)

• α “alpha” = significance level in hypothesis test, or acceptable probability of a Type I error (probability you can live with); 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
• σ “sigma-sub-x-bar” = standard error of the mean (abbreviated SEM)
• σ “sigma-sub-p-prime” = standard error of the proportion (abbreviated SEP)
• “sigma” = summation. (This is upper-case sigma. Lower-case sigma means standard deviation of a population; see the table above.) Be careful with the order of operations, such as ∑x² versus (∑x)².
• χ² “chi-squared” = distribution for multinomial experiments and contingency tables

This page is used in instruction at Tompkins Cortland Community College in Dryden, New York; it’s not an official statement of the College. Please visit www.tc3.edu/instruct/sbrown/ to report errors or ask to copy it.

For updates and new info, go to http://www.tc3.edu/instruct/sbrown/stat/