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Central Tendency, Dispersion, Correlation, Regression, Index Number, Time Series

### Transcript of Qam formulas

• 1. Quantitative Applications In ManagementFaculty Mr.Ashu JainCourse Quantitative Applications In Management.Programme MBA-IB; 1st Semester Amity International Business School

2. Arithmetic Mean (DirectMethod) Individual Series x = X / N Here X = Sum of variables And N = Number of Items Discrete Series x = fX / f Here f = Total no of Frequencies Continuous Series x = fX / f Here X = Mid values of class intervals 3. Arithmetic Mean (Short cut Method) Individual Series x = A + dx / N Here dx = Sum of deviations taken from assumed mean A = Assumed Mean Discrete Series x = A + (fdx) / f Here fdx = Sum of Multiplication of Frequency with deviations taken from assumed mean Continuous Series x = A + (fdx) / f 4. Median Individual Series N+1 / 2th Item Here N = Total No. of Items arranged in ascending or descending order. Discrete Series f+1 / 2th Item Here (f+1 / 2th) Item will be judged on the basis of cumulativefrequency. Continuous Series N / 2th Item L1 + N/2 C.F. * i F Here L1 = Lower limit of Median class N/2 = Median item C.F. = Cumulative Frequency preceding class interval F = Frequency against Median class interval i = Gap of Median class interval 5. Mode Continuous Series L1 +| f1 f 0 l * i | f1-f0 | + | f1-f2 | Here L = Lower limit of the Modal Class1 Interval. f = Frequency of Modal class1 6. Quartile Deviation Q.D. = Q Q / 2 3 1 Here, Q3 = 3rd quartile And, Q1 = 1st quartile 7. Mean Deviation / Average Deviation Individual Series M.D. =( ldxl ) / N Here, dx = X Mean / Median / Mode Discrete Series, Continuous Series M.D. =( f ldxl ) / f Here, dx = X Mean / Median / Mode 8. Standard Deviation Individual Series S.D. = dx / N Here, dx = X Actual Mean Discrete Series S.D. = fdx / f Here, dx = X Actual Mean Continuous Series S.D. = fdx / f Here, dx = X Actual Mean And, X = Mid Values of class intervals 9. Variance and Coefficient of Variation Variance = (S.D.) Coefficient of Variation = S.D. X 100 Mean 10. Karl Pearsons Coefficient ofCorrelation (Direct Method) r = dxdy N x y r= dxdy dx dy 11. Karl Pearsons Coefficient of Correlation(Short cut / Assumed Mean Method)o r = dxdy - dxdy N dx - (dx) dy - (dy) NN r = fdxdy (fdx)(fdy)N fdx - (fdx) fdy - (fdy)NN 12. Spearmans Rank Correlation Method When Ranks are not Repeated:- rk = 1 - 6 D N(N-1) Here D = Rank 1 Rank 2 13. Regression Equations General Form:- X on Y X X = r x (Y Y)y r x = bxy = Regression Coefficient of Equation X on Yy Y on X Y Y = r y (X X)x r y = byx = Regression Coefficient of Equation Y on Xx 14. Regression Equations Actual Mean Method:- X on Y X X = dxdy (Y Y) dy Y on X Y Y = dxdy (X X)dx 15. Regression Equations Assumed Mean Method:- X on Y X X = dxdy - dxdy (Y Y) Ndy - (dy) N Y on X Y Y = dxdy - dxdy (X X) N dx - (dx)N 16. Regression Equations Assumed Mean Method ( Continuous Series ) :- X on Y X X = fdxdy - fdxfdy(Y Y)N x ix fdy - (fdy)iyN Y on X Y Y = fdxdy - fdxfdy (X X)N x iy fdx - (fdx)ixN 17. Simple Aggregative Methodo P01 = P1 x 100P0Here, P01 = Price Index for the Current year P1 = Total of Current year Prices P0 = Total of Base year Prices P01 = (P1/ P0 x 100)NHere, P01 = Price Index for the Current year P1 = Current year Price P0 = Base year Price N = Total Number of Years 18. Chain Base IndexChain Base Index =Current year Link Relative x Previous year Chain Index100 19. Base ShiftingNew Base Index Number =Old Index Number of Current Year x 100Old Index Number of New Base Year 20. Laspeyres Method / AggregateExpenditure Methodo P01 = P1Q0 x 100P0Q0 21. Paasches Methodo P01 = P1Q1 x 100P0Q1 22. Dorbish and Bowleys Methodo P01 = P1Q0 + P1Q1P0Q0 P0Q1 x 1002 23. Marshall-Edgeworths Methodo P01 = P1Q0 + P1Q1 x 100P0Q0 + P0Q1 24. Fishers Methodo P01 = P1Q0 x P1Q1 x 100P0Q0 P0Q1 25. Kellys Methodo P01 = P1Q x 100P0Q Here, Q = Q0 + Q1 2 26. Weighted Average of Price Relative /Family Budget Method P01 = PVV Here, P = Price Relatives V = P0Q0 27. Components of Time Series Secular Trend Cyclical Variations Seasonal Variations Irregular or Random Variations 28. Methods of Measuring Trend Free Hand Curve Method Semi Average Method Moving Average Method Method of Least Square 29. Semi Average Method Annual Change =Difference of Two Semi Average ValuesDifference of Years of Semi Average 30. Method of Least Squareo Equation for Time Series Y = a + bXTo calculate a and b, Solve the following Equations:Y = aN + bXXY = aX + bXHere,Y = Given Data i.e. Sales or Profit etc.X= Years in terms of Units like 1,2,3 etc.