Statistics 1st PUC By Prof. Vipin Formula Book This contains formulae of units 3 onwards as per Karnataka Pre-University Syllabus. May also be useful for CBSE and ICSE. [Type the document subtitle] Classification and Tabulation Correction Factor Range Width of Class Class Midpoint Frequency Density Relative Frequency Page 2 www.VipinMKS.com Diagrammatic and Graphic Presentation of Data Percentage Bar Diagram Pie Diagram Page 3 www.VipinMKS.com 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 Page 4 www.VipinMKS.com 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 Page 5 www.VipinMKS.com Geometric Mean a) For Ungrouped Data b) For grouped data Harmonic Mean a) For Discrete and Continuous data Page 6 www.VipinMKS.com 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 Page 7 www.VipinMKS.com Use the formulae Page 8 www.VipinMKS.com 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 Page 9 www.VipinMKS.com 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 Page 10 www.VipinMKS.com Deviation method b) Grouped data x Deviation method c) Continuous data x x is the midpoint Deviation method Page 11 www.VipinMKS.com Page 12 www.VipinMKS.com 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 Page 13 www.VipinMKS.com Skewness Karl Pearson’s Coefficient of Skewness x Bowley’s Coefficient of Skewness Page 14 www.VipinMKS.com Page 15 www.VipinMKS.com 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 Page 16 www.VipinMKS.com Regression Analysis Regression Equation y x a) For ungrouped data b) For grouped data Page 17 www.VipinMKS.com Associates of Attributes Yule’s Coefficient of Association Page 18 www.VipinMKS.com 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 Page 19 www.VipinMKS.com 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 Page 20 www.VipinMKS.com Random Variable Mathematical Expression of Discrete Random Variable For Variance Addition Theorem Multiplication Theorem Coefficient of Correlation Page 21 www.VipinMKS.com