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Following table shows the usage of various symbols used in Statistics
Capitalization
Generally lower case letters represent the sample attributes and capital case letters are used to represent population attributes.
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$ P $ – population proportion.
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$ p $ – sample proportion.
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$ X $ – set of population elements.
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$ x $ – set of sample elements.
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$ N $ – set of population size.
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$ N $ – set of sample size.
Greek Vs Roman letters
Roman letters represent the sample attributs and greek letters are used to represent Population attributes.
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$ mu $ – population mean.
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$ bar x $ – sample mean.
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$ delta $ – standard deviation of a population.
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$ s $ – standard deviation of a sample.
Population specific Parameters
Following symbols represent population specific attributes.
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$ mu $ – population mean.
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$ delta $ – standard deviation of a population.
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$ {mu}^2 $ – variance of a population.
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$ P $ – proportion of population elements having a particular attribute.
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$ Q $ – proportion of population elements having no particular attribute.
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$ rho $ – population correlation coefficient based on all of the elements from a population.
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$ N $ – number of elements in a population.
Sample specific Parameters
Following symbols represent population specific attributes.
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$ bar x $ – sample mean.
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$ s $ – standard deviation of a sample.
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$ {s}^2 $ – variance of a sample.
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$ p $ – proportion of sample elements having a particular attribute.
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$ q $ – proportion of sample elements having no particular attribute.
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$ r $ – population correlation coefficient based on all of the elements from a sample.
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$ n $ – number of elements in a sample.
Linear Regression
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$ B_0 $ – intercept constant in a population regression line.
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$ B_1 $ – regression coefficient in a population regression line.
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$ {R}^2 $ – coefficient of determination.
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$ b_0 $ – intercept constant in a sample regression line.
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$ b_1 $ – regression coefficient in a sample regression line.
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$ ^{s}b_1 $ – standard error of the slope of a regression line.
Probability
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$ P(A) $ – probability that event A will occur.
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$ P(A|B) $ – conditional probability that event A occurs, given that event B has occurred.
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$ P(A”) $ – probability of the complement of event A.
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$ P(A cap B) $ – probability of the intersection of events A and B.
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$ P(A cup B) $ – probability of the union of events A and B.
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$ E(X) $ – expected value of random variable X.
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$ b(x; n, P) $ – binomial probability.
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$ b*(x; n, P) $ – negative binomial probability.
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$ g(x; P) $ – geometric probability.
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$ h(x; N, n, k) $ – hypergeometric probability.
Permutation/Combination
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$ n! $ – factorial value of n.
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$ ^{n}P_r $ – number of permutations of n things taken r at a time.
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$ ^{n}C_r $ – number of combinations of n things taken r at a time.
Set
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$ A Cap B $ – intersection of set A and B.
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$ A Cup B $ – union of set A and B.
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$ { A, B, C } $ – set of elements consisting of A, B, and C.
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$ emptyset $ – null or empty set.
Hypothesis Testing
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$ H_0 $ – null hypothesis.
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$ H_1 $ – alternative hypothesis.
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$ alpha $ – significance level.
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$ beta $ – probability of committing a Type II error.
Random Variables
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$ Z $ or $ z $ – standardized score, also known as a z score.
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$ z_{alpha} $ – standardized score that has a cumulative probability equal to $ 1 – alpha $.
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$ t_{alpha} $ – t statistic that has a cumulative probability equal to $ 1 – alpha $.
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$ f_{alpha} $ – f statistic that has a cumulative probability equal to $ 1 – alpha $.
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$ f_{alpha}(v_1, v_2) $ – f statistic that has a cumulative probability equal to $ 1 – alpha $ and $ v_1 $ and $ v_2 $ degrees of freedom.
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$ X^2 $ – chi-square statistic.
Summation Symbols
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$ sum $ – summation symbol, used to compute sums over a range of values.
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$ sum x $ or $ sum x_i $ – sum of a set of n observations. Thus, $ sum x = x_1 + x_2 + … + x_n $.
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