Qam formulas

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

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Qam formulas

  1. 1. Quantitative Applications In Management Faculty – Mr. Ashu Jain Course – “Quantitative Applications In Management.” Programme – MBA-IB; 1st Semester Amity International Business School
  2. 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. 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. 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 cumulative frequency. 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. 5. Mode Continuous Series  L1 + | f1 – f 0 l * i | f1-f0 | + | f1-f2 |  Here L = Lower limit of the Modal Class 1 Interval.  f = Frequency of Modal class 1
  6. 6. Quartile Deviation Q.D. = Q – Q / 2 3 1  Here, Q3 = 3rd quartile  And, Q1 = 1st quartile
  7. 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. 8. Standard Deviation Individual Series  S.D. = √∑dx² / N  Here, dx = X – Actual Mean Discrete Series  S.D. = √∑fdx² / ∑f  Here, dx = X – Actual Mean Continuous Series  S.D. = √∑fdx² / ∑f  Here, dx = X – Actual Mean And, X = Mid Values of class intervals
  9. 9. Variance and Coefficient of Variation Variance = (S.D.)² Coefficient of Variation = S.D. X 100 Mean
  10. 10. Karl Pearson’s Coefficient ofCorrelation (Direct Method) r = ∑dxdy N σx σy r= ∑dxdy √∑dx² √∑dy²
  11. 11. Karl Pearson’s Coefficient of Correlation(Short cut / Assumed Mean Method)o r = ∑dxdy - ∑dx∑dy N √∑dx² - (∑dx)² √∑dy² - (∑dy)² N N r = ∑fdxdy – (∑fdx)(∑fdy) N √∑fdx² - (∑fdx)² √∑fdy² - (∑fdy)² N N
  12. 12. Spearman’s Rank Correlation Method When Ranks are not Repeated:- rk = 1 - 6 ∑D² N(N²-1)  Here D = Rank 1 – Rank 2
  13. 13. Regression Equations General Form:-  X on Y X – X = r σx (Y – Y) σy• r σx = bxy = Regression Coefficient of Equation X on Y σy  Y on X Y – Y = r σy (X – X) σx• r σy = byx = Regression Coefficient of Equation Y on X σx
  14. 14. Regression Equations Actual Mean Method:-  X on Y X – X = ∑dxdy (Y – Y) ∑dy²  Y on X Y – Y = ∑dxdy (X – X) ∑dx²
  15. 15. Regression Equations Assumed Mean Method:-  X on Y X – X = ∑dxdy - ∑dx∑dy (Y – Y) N ∑dy² - (∑dy)² N  Y on X Y – Y = ∑dxdy - ∑dx∑dy (X – X) N ∑dx² - (∑dx)² N
  16. 16. Regression Equations Assumed Mean Method ( Continuous Series ) :-  X on Y X – X = ∑fdxdy - ∑fdx∑fdy (Y – Y) N x ix ∑fdy² - (∑fdy)² iy N  Y on X Y – Y = ∑fdxdy - ∑fdx∑fdy (X– X) N x iy ∑fdx² - (∑fdx)² ix N
  17. 17. Simple Aggregative Methodo P01 = ∑P1 x 100 ∑P0 Here,  P01 = Price Index for the Current year  ∑P1 = Total of Current year Prices  ∑P0 = Total of Base year Prices P01 = ∑(P1/ P0 x 100) N Here,  P01 = Price Index for the Current year  ∑P1 = Current year Price  ∑P0 = Base year Price  N = Total Number of Years
  18. 18. Chain Base IndexChain Base Index = Current year Link Relative x Previous year Chain Index 100
  19. 19. Base ShiftingNew Base Index Number = Old Index Number of Current Year x 100 Old Index Number of New Base Year
  20. 20. Laspeyre’s Method / AggregateExpenditure Methodo P01 = ∑P1Q0 x 100 ∑P0Q0
  21. 21. Paasche’s Methodo P01 = ∑P1Q1 x 100 ∑P0Q1
  22. 22. Dorbish and Bowley’s Methodo P01 = ∑P1Q0 + ∑P1Q1 ∑P0Q0 ∑P0Q1 x 100 2
  23. 23. Marshall-Edgeworth’s Methodo P01 = ∑P1Q0 + ∑P1Q1 x 100 ∑P0Q0 + ∑P0Q1
  24. 24. Fisher’s Methodo P01 =√ ∑P1Q0 x ∑P1Q1 x 100 ∑P0Q0 ∑P0Q1
  25. 25. Kelly’s Methodo P01 = ∑P1Q x 100 ∑P0Q Here, Q = Q0 + Q1 2
  26. 26. Weighted Average of Price Relative /Family Budget Method P01 = ∑PV ∑V Here, P = Price Relatives V = P0Q0
  27. 27. Components of Time Series Secular Trend Cyclical Variations Seasonal Variations Irregular or Random Variations
  28. 28. Methods of Measuring Trend Free Hand Curve Method Semi Average Method Moving Average Method Method of Least Square
  29. 29. Semi Average Method Annual Change =Difference of Two Semi Average ValuesDifference of Years of Semi Average
  30. 30. Method of Least Squareo Equation for Time Series Y = a + bXTo calculate a and b, Solve the following Equations: ∑Y = aN + b∑X ∑XY = a∑X + b∑X²Here, Y = Given Data i.e. Sales or Profit etc. X= Years in terms of Units like 1,2,3 etc.

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