STATISTICS FORMULAS
Statistics is essentially the process of learning from data. The goal of statistics is to make correct statements
or inferences about a population based on a sample.
This handout consists of terminology and formulas contained in Essentials of Statistics (3rd edition) by Mario
Triola.
Chapter 3 – Terminology and formulas utilized in Descriptive Statistics:

x
is the variable usually used to represent the individual data values
n
represents the number of values in a sample
N
represents the number of values in a population
x
x
u
Denotes the addition of a set of values
is the mean of a set of sample values
n
x
is the mean of all values in a population
n
f
x
is the frequency of occurrence of a given data variable range
(ie 60 to 69)
f x
is the product of the frequency of occurrence and the midpoint of the range
 x f
f
denotes the mean of the frequency distribution
z
xu
denotes the z score

 x  x 
2
s
standard deviation
n  1
n x 2    x 
2
s
s

standard deviation shortcut
nn  1
   f  x
n  f  x2  
2
nn  1
v  s2
standard deviation for frequency distribution
variance
The Academic Support Center at Daytona State College (Math 67 pg 1 of 4)
STATISTICS FORMULAS
(continued)
Chapter 4 – Terminology and formulas utilized in Probabilities:
P
denotes a probability
denote specific events
denotes the probability of event A occurring
A, B, C
P A
P  A 
number of times A occurred
relative frequency approximation of probability
number of times trial was repeated
P  A 
number of ways A can occur s

number of different events
n
classic approach to probability
P A or B  P A  PB if A, B are mutually exclusive
P( A or B)  P A  PB  P A and B if A, B are not mutually exclusive
P( A and B)  P A  PB if A, B are independent
P A and B  P A  PB A If A, B are dependent
n!
Permutations (no elements alike)
n Pr 
n  r !
n
Pr 
n!
Permutations ( n1 alike, …)
n1!n 2 !...nk !
n
Cr 
n!
Combinations
n  r !r !
Chapter 5 – Terminology and formulas utilized in Probability Distributions:
u   x  Px  mean probability distribution

 x
Px  
2

 Px   u 2 standard deviation (probability distribution)
n!
 p x q n  x binomial probability
n  x ! x !
u  n p
mean binomial
 2  n  p  q variance binomial
  n  p  q standard deviation binomial
The Academic Support Center at Daytona State College (Math 67 pg 2 of 4)
STATISTICS FORMULAS
(continued)
Chapter 6 – Terminology and formulas utilized in Normal Distribution:
z
xx
xu
standard score
or
s

ux  u
x 
central limit theorem

central limit theorem (standard error)
n
Chapter 7 – Terminology and formulas utilized in Sample Size Determination:
^ ^
^
^
p  E  p  p  E proportion where E  z
x  E  u  x  E mean where E  z 2
n  1s 2
x2R
2 
n  1s 2
x2L

n
2
pq
n
if  is known or E  t
s
2
variance
Chapter 7 – Terminology and formulas utilized in Confidence Intervals:
z 
n
 0.25
z 
n
pq
2
 2
E2
2
 2
^
^
proportion ( p and q are not known)
^ ^
E2
 z 2 
n

 E 
^
^
proportion ( p and q are known)
2
mean
The Academic Support Center at Daytona State College (Math 67 pg 3 of 4)
n
if  is unknown
STATISTICS FORMULAS
(continued)
Chapter 8 – Terminology and formulas utilized in Test Statistics (one population):
^
z
z
p p
pq
n
xu

proportion – one population
mean – one population ( 
known )
n
t
xu
s
n
x2 
n  1s 2
2
mean – one population ( 
unknown )
standard deviation or variance– one population
The Academic Support Center at Daytona State College (Math 67 pg 4 of 4)