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Normal Distribution
� Properties of a random variable 1 . � : Mean 2 . � : Standard deviation
2
X ~ N ( �� , ) following normal distribution :
3 . The mean , the median and the mode are the same 4 . The normal curve representing the distribution is a bell-shaped curve which is symmetric about the middle vertical line 5 . P ( X � �) � P ( X � �) � 0.5 6 . The total area under the curve is 1
� Standardization of a normal variable : 1 .
2 .
Z
2
~ N ( 0,1 ) deviation 1
X � � Z � for �
: Standard normal distribution with mean 0 and standard
2
X ~ N ( �� , )
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Bivariate Analysis
� Correlations :
Positive
Negative
where r is the correlation coefficient
Strong 0.75 �r
� 1
Moderate 0.5 �r
� 0.75
Weak 0 �r
� 0.5
No r � 0
Weak �0.5 � r � 0
Moderate �0.75 � r � � 0.5
Strong �1� r � � 0.75
� Linear regression : 1 . y �ax � b : Regression line of y on x
2 . x �ay � b : Regression line of x on y
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