# Stats without Tears

Statistics Symbol Sheet

Updated 5 Nov 2020
(What’s New?)

Copyright © 2002–2024 by Stan Brown, BrownMath.com

Statistics Symbol Sheet

Updated 5 Nov 2020
(What’s New?)

Copyright © 2002–2024 by Stan Brown, BrownMath.com

Print:

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 |
---|---|---|

n |
N |
number of members of sample or population |

x̅ “x-bar” |
μ “mu” or μ _{x} |
mean |

M or Medor x̃ “x-tilde” |
(none) | median |

s
(TIs say Sx) |
σ “sigma”
or σ _{x} |
standard deviation For 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,
σ_{x̅} (“sigma sub x-bar”) is the standard deviation of
sample means, or standard error of the mean.

*b*=*y*intercept of a line. Defined here in Chapter 4. (Some statistics books use*b*_{0}.)- 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.
*H*= null hypothesis. Defined here in Chapter 10._{o}*H*or_{1}*H*= alternative hypothesis. Defined here in Chapter 10._{a}*IQR*= interquartile range, Q_{3}−Q_{1}. 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*b*_{1}.)*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(
*A*^{C}) 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*P*= 80th percentile (_{80}*Pk*or*P*=_{k}*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*Q*= first quartile (_{1}*Q3*or*Q*= third quartile) Defined here in Chapter 3._{3}*r*= linear correlation coefficient of a sample. Defined here in Chapter 4.*R*² = 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
σ
_{x̅}). Defined here in Chapter 8. - SEP = standard error of the proportion (symbol is
σ
_{p̂}). 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*z*_{area}= 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.)

- 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.
- σ
_{x̅}“sigma-sub-x-bar”; see SEM above. - σ
_{p̂}“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.

**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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