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 Pearsons Beta and Gamma Coefficients

Also

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Skewness

Karl Pearsons Coefficient of Skewness

x

Bowleys Coefficient of Skewness

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Analysis of Bi-Variate Data

Karl Pearsons Coefficient of Correlation

a) For ungrouped data

b) For Grouped data

Spearmans 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

Yules 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