statistics 1st puc formula book - professor...
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Statistics 1st PUC Formula Book
By Prof. Vipin This contains formulae of units 3 onwards as per Karnataka Pre-University Syllabus. May also be useful for CBSE and ICSE.
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Classification and Tabulation
Correction Factor
Range
Width of Class
Class Midpoint
Frequency Density
Relative Frequency
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Diagrammatic and Graphic Presentation of Data
Percentage Bar Diagram
Pie Diagram
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Analysis of Uni-variate Data
Arithmetic Mean
a) Direct Method (Ungrouped data)
x
b) Deviation Method (Ungrouped data)
x
c) Discrete Data (grouped data)
x
d) Deviation method (grouped data)
x
e) Step Deviation (Continuous Data)
x
Weighted Arithmetic Mean
x
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Median
a) Ungrouped data
b) Discrete (grouped)
c) Continuous data
Mode
a) Ungrouped data: Mode is the value which is highest o the distribution
b) Discrete Data
c) Continuous data
Empirical Relation Between Mean, Median and Mode
x
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Geometric Mean
a) For Ungrouped Data
b) For grouped data
Harmonic Mean
a) For Discrete and Continuous data
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Partition Values (Measures of Position)
Computation of Quartiles, Deciles and Percentiles
a) Ungrouped Data
1) Arrange data in order. Then use the following
b) Discrete (Grouped)
1) Find LCF. Then use the following
c) Discrete (Continuous)
1) Find LCF.
2) Find
where N denotes total frequency.
3) Qi, Di, Pi class = class corresponding to LCF just
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Use the formulae
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Measures of Dispersion
Coefficient of Range
Quartile Deviation
Coefficient of Quartile Deviation
Mean Deviation
a) Ungrouped data
x
b) Grouped data
x x
c) Continuous data
x x
x
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Computation of M.D from Median
a) Ungrouped data
b) Discrete data
c) Continuous data
Computation of M.D from Mode
a) Ungrouped data
b) Discrete data
Standard Deviation
a) Ungrouped data
x
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Deviation method
b) Grouped data
x
Deviation method
c) Continuous data
x
x is the midpoint
Deviation method
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Moments
Raw Moment
Central Moment
a) First
x
b) Second
x
c) Third
x
d) Fourth
x
Karl Pearson’s Beta and Gamma Coefficients
Also
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Skewness
Karl Pearson’s Coefficient of Skewness
x
Bowley’s Coefficient of Skewness
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Analysis of Bi-Variate Data
Karl Pearson’s Coefficient of Correlation
a) For ungrouped data
b) For Grouped data
Spearman’s Coefficient of Rank Correlation
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Regression Analysis
Regression Equation
y x
a) For ungrouped data
b) For grouped data
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Associates of Attributes
Yule’s Coefficient of Association
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Interpolation and Extrapolation
Binomial Expansion
Expansion Equation to be Taken
(y-1)2 y2-2y1+y0=0
(y-1)3 y3-3y2+3y1=0
(y-1)4 y4-4y3+6y2-4y1+y0=0
(y-1)5 y5-5y4+10y3-10y2+5y1-y0=0
(y-1)6 y6-6y5+15y4-20y3+15y2-6y1+y0=0
(y-1)7 y7-7y6+21y5-35y4+35y3-21y2+7y1=0
(y-1)8 y8- 8y7+28y6- 56y5+70y4-56y3+28y2-8y1+y0
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Probability Theory
Statistical Definition
Classical Definition
Axiomatic Definition
Probability of Occurrence of at Least One of Two / Three Events
Probability of two Mutually Exclusive Events
Conditional Probability
Multiplication of Probability of Two / Three Dependent Events
Multiplication of Probability of Two Independent Events
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Random Variable
Mathematical Expression of Discrete Random Variable
For Variance
Addition Theorem
Multiplication Theorem
Coefficient of Correlation