Here you will find the most common statistics equations and formulas used in high school and fundamental university courses. These include basic statistical measures and probability formulas. For more calculus based statistics formulas, please see here.
Where x_{i} are all the individual data points, and N is the number of points being averaged
x̄  =  ∑ 

= 

The middle value in the set of numbers that are arranged in ascending order. If there are an even number of values, the median is the average of the two middle values.
If n is odd  ( 

)  th term 
If n is even  ( 

)  th term  +  ( 

+ 1  )  th term 
The most frequently occurring value in the set of values
+ Means an increase
 Means a decrease
% Change = 

Ă—100% 
Standard Deviation is one measure of how spread the data is.
Sample  S =  √ 

Where x̄ is the sample mean and n is the number of observations
Population  σ =  √ 

Where μ̄ is the population mean and n is the number of observations
Variance is one measure of how spread the data is. It is the standard deviation squared.
Sample  S ^{2} = 

Where x̄ is the sample mean and n is the number of observations
Population  σ ^{2} = 

Where μ̄ is the population mean and n is the number of observations
Covariance is a measure of two variablesâ€™ joint variability, or how they will vary together.
Sample  Cov(x,y) = 

The measure of variance between variables x and y, where x̄ is the sample mean of the x values, ȳ is the mean of the y values, and n is the number of observations
Population  Cov(x,y) = 

Chi Squared tells you the difference between your observations and what you expected.
X^{2} =  ∑ 

Where O_{i} is the observed value and E_{i} is the expected value
P(A) = 

Where f is the frequency of the event and n is the sample size
In other words, the probability of A not occurring.
P(Not A) = 1  P(A) 
In other words, the probability of A and B occurring independently.
P(A and B) = P(A) * P(B) 
To be used when one event A affects the probability of event B.
P(A and B) = P(A) * P(B given A) 
P(A and B) = P(B) * P(A given B) 
For example,
Drawing marbles out of the box without replacement will affect the probability of drawing a marble of a certain color.
In other words, the probability of either A or B occurring.
P(A or B) = P(A) + P(B) 
In other words, the probability of either A or B occurring.
P(A or B) = P(A) + P(B)  P(A and B) 
Expected Value is the final predicted value of a variable, computed by multiplying each possible value by its probability and summing it.
E[x] =  ∑  x_{i}P  (  x_{i}  ) 
Where x_{i} are the values of x and P(x_{i}) are the probabilities of each value