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Statistics Formulas
R = H – L
Range
MR 
LH
2
Midrange
ML 
n 1
2
Median Locator
x
x
s
2
i
Sample Mean
n
 x

 x
2
i
Definition of Sample Variance
n 1
 x 
x  n
2
s2 
i
2
i
Calculating Formula for Sample Variance
n 1
s  s2
Definition of Sample Standard Deviation
 x 
x  n
2
s
i
2
i
n 1
xnew  a  bx
z
x

Calculating Formula for Sample Standard Deviation
Linear Transformation
x = σz + 
IQR = Q3 – Q1
z-score
Interquartile Range
Probability
P(AC) = 1 – P(A)
Complement Rule
P(A or B) = P(A) + P(B) – P(A and B)
P(A and B) = P(A)P(B|A)
P(A and B) = P(B)P(A|B)
P( B | A) 
P( AandB)
P( A)
Addition Rule
Multiplication Rule
Multiplication Rule
Conditional Probability
Binomial Distribution
n
p( x)    p x (1  p) n  x , x = 0, 1, …, n
 x
pˆ 
x2
~
p
is Wilson’s Estimate
n4
x
is the sample proportion
n
x
Sampling Distributions of
Parameter

Estimator
and
p̂
Mean
Of Estimator
x
 X  np(1  p)
X = np
Standard Deviation
of Estimator

X
z-score
z
n
x

n
p
p̂
p(1  p)
n
p
z
pˆ  p
p (1  p )
n
Inference Formulas
Parameter

Confidence Interval
xz
*
Test Statistic

z
n
x  o

n
s
, df  n  1
n

x t
p
~
p (1  ~
p)
*
~
pz
n4
*
t
z
x  o
, df  n  1
s
n
pˆ  p0
p0 (1  po )
n
Sample Size Determination Formulas
Parameter
Formula

 z *
n  
 m
p



2
2
 z*  *
n  4    p (1  p * )
m
z Tests
Research
Hypothesis
P-value
Rejection
Region
Ha:  > o
P(Z > z)
Z > zα
Ha:  < o
P(Z < z)
Z < -zα
Ha:   o
2P(Z > |z|)
Z < -zα/2 or Z > zα/2
Ha: p < po
P(Z < z)
Z < -zα
Ha: p > po
P(Z > z)
Z > zα
Ha: p  po
2P(Z > |z|)
Z < -zα/2 or Z > zα/2
t Tests
Research
Hypothesis
P-value
Rejection
Region
Ha:  > o
P(T > t)
t > tα
Ha:  < o
P(T < t)
t < -tα
Ha:   o
2P(T > |t|)
t < -tα/2 or t > tα/2