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14.1 Symbols and their meanings

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This module defines symbols used throughout the Collaborative Statistics textbook.
Symbols and their meanings
Chapter (1st used) Symbol Spoken Meaning
Sampling and Data The square root of same
Sampling and Data π Pi 3.14159… (a specific number)
Descriptive Statistics Q1 Quartile one the first quartile
Descriptive Statistics Q2 Quartile two the second quartile
Descriptive Statistics Q3 Quartile three the third quartile
Descriptive Statistics IQR inter-quartile range Q3-Q1=IQR
Descriptive Statistics x ¯ x-bar sample mean
Descriptive Statistics μ mu population mean
Descriptive Statistics s s x sx s sample standard deviation
Descriptive Statistics s 2 s x 2 s-squared sample variance
Descriptive Statistics σ σ x σx sigma population standard deviation
Descriptive Statistics σ 2 σ x 2 sigma-squared population variance
Descriptive Statistics Σ capital sigma sum
Probability Topics { } brackets set notation
Probability Topics S S sample space
Probability Topics A Event A event A
Probability Topics P ( A ) probability of A probability of A occurring
Probability Topics P ( A ∣ B ) probability of A given B prob. of A occurring given B has occurred
Probability Topics P ( A or B ) prob. of A or B prob. of A or B or both occurring
Probability Topics P ( A and B ) prob. of A and B prob. of both A and B occurring (same time)
Probability Topics A' A-prime, complement of A complement of A, not A
Probability Topics P ( A' ) prob. of complement of A same
Probability Topics G 1 green on first pick same
Probability Topics P ( G 1 ) prob. of green on first pick same
Discrete Random Variables PDF prob. distribution function same
Discrete Random Variables X X the random variable X
Discrete Random Variables X~ the distribution of X same
Discrete Random Variables B binomial distribution same
Discrete Random Variables G geometric distribution same
Discrete Random Variables H hypergeometric dist. same
Discrete Random Variables P Poisson dist. same
Discrete Random Variables λ Lambda average of Poisson distribution
Discrete Random Variables ≥ greater than or equal to same
Discrete Random Variables ≤ less than or equal to same
Discrete Random Variables = equal to same
Discrete Random Variables ≠ not equal to same
Continuous Random Variables f ( x ) f of x function of x
Continuous Random Variables pdf prob. density function same
Continuous Random Variables U uniform distribution same
Continuous Random Variables Exp exponential distribution same
Continuous Random Variables k k critical value
Continuous Random Variables f ( x ) = f of x equals same
Continuous Random Variables m m decay rate (for exp. dist.)
The Normal Distribution N size 12{N} {} normal distribution same
The Normal Distribution z size 12{z} {} z-score same
The Normal Distribution Z size 12{Z} {} standard normal dist. same
The Central Limit Theorem CLT size 12{ ital "CLT"} {} Central Limit Theorem same
The Central Limit Theorem X X-bar the random variable X-bar
The Central Limit Theorem μ x size 12{μ rSub { size 8{x} } } {} mean of X the average of X
The Central Limit Theorem μ x ¯ size 12{μ rSub { size 8{ {overline {x}} } } } {} mean of X-bar the average of X-bar
The Central Limit Theorem σ x size 12{σ rSub { size 8{x} } } {} standard deviation of X same
The Central Limit Theorem σ x ¯ size 12{σ rSub { size 8{ {overline {x}} } } } {} standard deviation of X-bar same
The Central Limit Theorem Σ X sum of X same
The Central Limit Theorem Σ x sum of x same
Confidence Intervals CL size 12{ ital "CL"} {} confidence level same
Confidence Intervals CI size 12{ ital "CI"} {} confidence interval same
Confidence Intervals EBM size 12{ ital "EBM"} {} error bound for a mean same
Confidence Intervals EBP size 12{ ital "EBP"} {} error bound for a proportion same
Confidence Intervals t size 12{t} {} student-t distribution same
Confidence Intervals df size 12{ ital "df"} {} degrees of freedom same
Confidence Intervals t α 2 student-t with a/2 area in right tail same
Confidence Intervals p' p ^ p-prime; p-hat sample proportion of success
Confidence Intervals q' q ^ q-prime; q-hat sample proportion of failure
Hypothesis Testing H 0 size 12{H rSub { size 8{0} } } {} H-naught, H-sub 0 null hypothesis
Hypothesis Testing H a size 12{H rSub { size 8{a} } } {} H-a, H-sub a alternate hypothesis
Hypothesis Testing H 1 size 12{H rSub { size 8{1} } } {} H-1, H-sub 1 alternate hypothesis
Hypothesis Testing α size 12{α} {} alpha probability of Type I error
Hypothesis Testing β size 12{β} {} beta probability of Type II error
Hypothesis Testing X1 ¯ − X2 ¯ size 12{ {overline {X1}} - {overline {X2}} } {} X1-bar minus X2-bar difference in sample means
μ 1 − μ 2 size 12{μ rSub { size 8{1} } - μ rSub { size 8{2} } } {} mu-1 minus mu-2 difference in population means
P ' 1 − P ' 2 size 12{P' rSub { size 8{1} } - P' rSub { size 8{2} } } {} P1-prime minus P2-prime difference in sample proportions
p 1 − p 2 size 12{p rSub { size 8{1} } - p rSub { size 8{2} } } {} p1 minus p2 difference in population proportions
Chi-Square Distribution Χ 2 Ky-square Chi-square
O Observed Observed frequency
E Expected Expected frequency
Linear Regression and Correlation y = a + bx y equals a plus b-x equation of a line
y ^ y-hat estimated value of y
r correlation coefficient same
ε error same
SSE Sum of Squared Errors same
1.9 s 1.9 times s cut-off value for outliers
F-Distribution and ANOVA F F-ratio F ratio
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Source:  OpenStax, Collaborative statistics: custom version modified by r. bloom. OpenStax CNX. Nov 15, 2010 Download for free at http://legacy.cnx.org/content/col10617/1.4
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