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Statistics Formulas

This is a collection of common formulas that you will use in statistics.

Table of Random Digits
Tables of random digits are important for a few applications in statistics. This is a table of 500 random digits that can be used for things such as the construction of a simple random sample.

The Gamma Function Formula
The gamma function shows up throughout mathematics, and especially in probability. Unlike some more elementary functions, the gamma function is defined as the integral of another function.

Correlation Coefficient
The correlation coefficient measures the strength of the relationship between two sets of data.

The Normal Distribution or Bell Curve
The normal distribution, commonly known as the bell curve occurs throughout statistics. Here you can see the equation for all bell curves.

Formulas & Tables
This is a collection of common formulas that you will use in statistics.

Z-Score Formula
Any bell curve can be transformed into the standard bell curve by using this formula.

The Standard Deviation Formula
The standard deviation is a measure of the spread of our data.

Standard Normal Distribution Table
At some point we need to find probabilities for normally distributed variables. A table of the standard normal distribution gives us the probability between any two z scores.

Student t Distribution Table
The Student t distribution is utilized in some instances when the standard normal distribution cannot be used. One way to perform calculations is to consult a table of critical values of the Student t distribution.

Formulas for Combinations and Permutations

Binomial Table
The binomial distribution is a probability distribution for certain discrete random variables. This table displays the probabilities for n =2 to 6.

Binomial Table
The binomial distribution is a probability distribution for certain discrete random variables.

Binomial Table
The binomial distribution is a probability distribution for certain discrete random variables.

Binomial Probability Distribution Formula

Addition Rules in Probability
The addition rule provides a way to calculate the probability of the union of two events.

What Is the Formula for the Chi-Square Statistic and How Do You Use It?

How to Derive the Formula for Combinations
It's one thing to memorize a formula, it's another to know where it comes from. See why the formula for a combination is what it is, just based upon some basic counting properties.

What Is the Formula for Expected Value
The formula for the expected value is relatively easy to compute. It simply involves several multiplications and additions.

Margin of Error Formula

Student's t Distribution Formula

Probability of the Union of Three or More Sets
The addition rules in probability are typically stated for two sets. These formulas can be generalized for three or more sets.

Sum of Squares Formula Shortcut
The sample standard deviation requires us to first calculate mean, then use this for the rest of the calculation. An equivalent formula allows us to not even know the mean

What Is a Table of Random Digits?
A table of random digits can be very helpful in the practice of statistics. See how such a table can be used.

Calculations with the Gamma Function
The gamma function is defined by a somewhat complicated formula. See how this formula is used to calculate the gamma function for certain values of z.

Birthday Problem Probabilities
This is a table of probabilities for the birthday problem, to see the probability that a room of 1 to 100 people share a birthday.

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