DEPARTMENT OF MATHEMATICS (Shift-II)
ST.JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI-620002
II B.Com-BUSINESS STATISTICS
FORMULAE
UNIT-II
Mean-Mode
.
Standard Devition
2. Bowley’s coefficient of Skewness Sk B  Q3  Q1  2 Median .
Q3  Q1
1. Karl Pearson’s coefficient of Skewness Sk P 
3. Karl Pearson’s Correlation Coefficient r 
 xy
 x2   y 2
.where x  X  X , y  Y  Y .
4. Karl Pearson’s Correlation Coefficient (Direct Method) r 
N  XY   X  Y
N  X   X   N Y 2  Y 
2
2
5. Spearman’s Rank Correlation Coefficient R  1 
6  D2
, where D  R1  R2
N3  N
ASSOCIATION OF ATTRIBUTES
A

Total
B
(AB)
(B )
(B)

( A )
(  )
( )
Total
(A)
( )
N
6. From the table, the following relationships can be described:
(A) = (AB) + ( A  ); (  ) = (  B ) + (  )
(B)= (AB) + (  B ) ;(  )=( A  )+(  )
N= (A) + (  ) = (B) + (  )
Methods of Studying Association
7. Comparison of Observed and Expected Frequencies Method
Attributes A and B are
(i)
Independent if ( AB)  ( A)  ( B) .
N
(ii)
(iii)
Positively Associated ( AB )  ( A )  ( B ) .
N
Negatively Associated ( AB )  ( A )  ( B ) .
N
Prepared by
Mr.Carmel Pushpa Raj.J
(Dept of Mathematics)
Page 1
2
.
8. Proportion Method
Attributes A and B are
(i)
Independent if ( AB )  ( A )  ( B ) .
(ii)
Positively Associated ( AB)  ( A)  ( B) .
( B)
( )
( B)
(iii)
( )
Negatively Associated ( AB)  ( A)  ( B) .
( B)
( )
9. Yule’s Coefficient of Association
Q
( AB)( )  ( A )( B)
.
( AB)( )  ( A )( B)
(i)
(ii)
(iii)
(iv)
If Q =1 then there is a perfect positive association.
If Q =  1 then there is a perfect negative association.
If Q =0 then attributes are independent.
If 1  Q  0 then the attributes are negatively associated.
(v)
If 0  Q  1 then the attributes are positively associated.
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“Mathematics may not Teach us how to add happiness or how to minus sadness.
But, it does teach one important thing. Every PROBLEM has a Solution”
Prepared by
Mr.Carmel Pushpa Raj.J
(Dept of Mathematics)
Page 2