Math Is Fun Forum

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Statistics Formulas

Statistics Formulas

Average (mean):

Binomial Probability Mass Function
The probability of getting exactly k successes out of n events where the probability of k on each event is p:

Mean:

Variance:

Standard deviation:

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Statistics Formulas

Poisson Distribution

Poisson distrubtion is the limiting form of the Binomial Distribution when n, the number of trials is very large, and p, the probability of success, is very small, np remains finite.
Let

A random variable X taking values 0,1,2 .. is said to have a Poisson distribution with parameter

if its proabability distribution is given by

where r=0,1,2....

The mean of the Poisson Distribution

The variance of the Poisson Distribution

The mean and the variance of the Poisson Distribution is equal to

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Statistics Formulas

Product Moment Correlation Coefficient (PMCC)

The least squares regression line

y = a + bx

    and   

Where

Last edited by Daniel123 (2008-03-22 13:32:39)

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Statistics Formulas

Normal Distribution Function

Last edited by Daniel123 (2008-04-15 08:14:04)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,395

Re: Statistics Formulas

Standard Deviation

where

and

is the mean.

Standard Deviation

where d = x - A, where A is the Assumed mean.

Standard Deviation for Discrete series:
In discrete series when deviations are taken from Arithmetic Mean,

where

and

is the mean.

When deviations are taken from Assumed mean,

where d = x - A and A is the Assumed mean.

Variance

Variance is the square of Standard Deviation. The positive square root of the variance is defined as Standard Deviation.

Standard Deviation for the first 'n' Natural numbers is

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.