Number of class intervals
Population covariance
= 1 + 3.3 log (n)
N

 ( x   )( y   )
i
Class width
L arg est Observatio n  SmallestObservation
Number of Classes
 xy 
n
 ( x  x )( y  y )
i
N

n
xi
x  i 1
n
 
Population coefficient of correlation
Range
= Largest observation - Smallest observation

 xy
 x y
Sample coefficient of correlation
Population variance
N
 (x  )
r 
2
i
i 1
s xy
sxsy
N
Coefficient of determination
Sample variance
R2 = r2
n
 (x  x)
2
i
s2 =
n 1
n
n


xi
yi 
 n
1 

i 1
s xy 
x i y i  i 1


n  1 i 1
n






Sample mean
2 =
i
i 1
s xy 
xi
i 1

y
Sample covariance
N
 =
i
N
Population mean

x
i 1
i 1
n 1
2

 n
 


xi  
n

 

1
 i 1
 

s 2x 
x i2 
n  1  i 1
n









Geometric Mean
Rg  n (1  R1 )(1  R2 )....(1  Rn )  1
Chebysheff’s Theorem
1
1
for k > 1
k2
Population Coefficient of Variation
Population standard deviation
CV 
 =
2
Sample standard deviation
s = s2


Sample Coefficient of Variation
s
cv  _
x
Location of a Percentile
L p  ( n  1)
P
100
Interquartile Range
= Q3 – Q1
Mean Absolute Deviation
n
 x x
i
MAD=
i 1
n
Conditional Probability
𝑃(𝐴|𝐵) =
𝑃(𝐴 𝑎𝑛𝑑 𝐵)
𝑃(𝐵)
Independence Events
P(A|B) = P(A)
or
P(B|A) = P(B)
Complement Rule
P(Ac) = 1 – P(A)
Please check the formula before copying
from this sheet.
Multiplication Rule
If you found any typo, please let me know.
These formulas are provided by the
Author/publisher.
P(A and B) = P(B) P(A|B)
or
P(A and B) = P(A) P(B|A)
Multiplication Rule for Independence Events
P( A and B) = P(A) P(B)
Addition Rule
P(A or B) = P(A) + P(B) – P(A and B)
Addition Rule for Mutually Exclusive Events
P(A or B) = P(A) + P(B)
Bayes’s Law
P ( Ai | B ) 
P ( Ai ) P ( B | Ai )
P ( A1 ) P ( B | A1 )  P ( A2 ) P ( B | A2 )  ...  P ( Ak ) P ( B | Ak )