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.

- $ P $ – population proportion.
- $ p $ – sample proportion.
- $ X $ – set of population elements.
- $ x $ – set of sample elements.
- $ N $ – set of population size.
- $ N $ – set of sample size.

## Greek Vs Roman letters

Roman letters represent the sample attributs and greek letters are used to represent Population attributes.

- $ \mu $ – population mean.
- $ \bar x $ – sample mean.
- $ \delta $ – standard deviation of a population.
- $ s $ – standard deviation of a sample.

## Population specific Parameters

Following symbols represent population specific attributes.

- $ \mu $ – population mean.
- $ \delta $ – standard deviation of a population.
- $ {\mu}^2 $ – variance of a population.
- $ P $ – proportion of population elements having a particular attribute.
- $ Q $ – proportion of population elements having no particular attribute.
- $ \rho $ – population correlation coefficient based on all of the elements from a population.
- $ N $ – number of elements in a population.

## Sample specific Parameters

Following symbols represent population specific attributes.

- $ \bar x $ – sample mean.
- $ s $ – standard deviation of a sample.
- $ {s}^2 $ – variance of a sample.
- $ p $ – proportion of sample elements having a particular attribute.
- $ q $ – proportion of sample elements having no particular attribute.
- $ r $ – population correlation coefficient based on all of the elements from a sample.
- $ n $ – number of elements in a sample.

## Linear Regression

- $ B_0 $ – intercept constant in a population regression line.
- $ B_1 $ – regression coefficient in a population regression line.
- $ {R}^2 $ – coefficient of determination.
- $ b_0 $ – intercept constant in a sample regression line.
- $ b_1 $ – regression coefficient in a sample regression line.
- $ ^{s}b_1 $ – standard error of the slope of a regression line.

## Probability

- $ P(A) $ – probability that event A will occur.
- $ P(A|B) $ – conditional probability that event A occurs, given that event B has occurred.
- $ P(A’) $ – probability of the complement of event A.
- $ P(A \cap B) $ – probability of the intersection of events A and B.
- $ P(A \cup B) $ – probability of the union of events A and B.
- $ E(X) $ – expected value of random variable X.
- $ b(x; n, P) $ – binomial probability.
- $ b*(x; n, P) $ – negative binomial probability.
- $ g(x; P) $ – geometric probability.
- $ h(x; N, n, k) $ – hypergeometric probability.

## Permutation/Combination

- $ n! $ – factorial value of n.
- $ ^{n}P_r $ – number of permutations of n things taken r at a time.
- $ ^{n}C_r $ – number of combinations of n things taken r at a time.

## Set

- $ A \Cap B $ – intersection of set A and B.
- $ A \Cup B $ – union of set A and B.
- $ \{ A, B, C \} $ – set of elements consisting of A, B, and C.
- $ \emptyset $ – null or empty set.

## Hypothesis Testing

- $ H_0 $ – null hypothesis.
- $ H_1 $ – alternative hypothesis.
- $ \alpha $ – significance level.
- $ \beta $ – probability of committing a Type II error.

## Random Variables

- $ Z $ or $ z $ – standardized score, also known as a z score.
- $ z_{\alpha} $ – standardized score that has a cumulative probability equal to $ 1 – \alpha $.
- $ t_{\alpha} $ – t statistic that has a cumulative probability equal to $ 1 – \alpha $.
- $ f_{\alpha} $ – f statistic that has a cumulative probability equal to $ 1 – \alpha $.
- $ 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.
- $ X^2 $ – chi-square statistic.

## Summation Symbols

- $ \sum $ – summation symbol, used to compute sums over a range of values.
- $ \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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