Qam formulas
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Transcript of Qam formulas
Quantitative Applications In Management
Faculty – Mr. Ashu Jain
Course – “Quantitative Applications In Management.”
Programme – MBA-IB; 1st Semester
Amity International Business School
Arithmetic Mean (Direct Method)
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
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
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
Mode
Continuous Series
L1 + |f1 – f0l * i
| f1-f0 | + | f1-f2 | Here L1 = Lower limit of the Modal Class
Interval. f1 = Frequency of Modal class
Quartile Deviation
Q.D. = Q3 – Q1 / 2
Here, Q3 = 3rd quartile And, Q1 = 1st quartile
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
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 MeanAnd, X = Mid Values of class intervals
Variance and Coefficient of Variation
Variance = (S.D.)²
Coefficient of Variation = S.D. X 100
Mean
Karl Pearson’s Coefficient of Correlation (Direct Method)
r = ∑dxdyN σx σy
r = ∑dxdy√∑dx² √∑dy²
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
Spearman’s Rank Correlation Method
When Ranks are not Repeated:-
rk = 1 - 6 ∑D²
N(N²-1)
Here D = Rank 1 – Rank 2
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
Regression Equations Actual Mean Method:-
X on Y
X – X = ∑dxdy (Y – Y) ∑dy²
Y on X
Y – Y = ∑dxdy (X – X) ∑dx²
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
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
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
Chain Base Index
Chain Base Index =
Current year Link Relative x Previous year Chain Index
100
Base Shifting
New Base Index Number =
Old Index Number of Current Year x 100
Old Index Number of New Base Year
Laspeyre’s Method / Aggregate Expenditure Method
o P01 = ∑P1Q0 x 100∑P0Q0
Paasche’s Method
o P01 = ∑P1Q1 x 100∑P0Q1
Dorbish and Bowley’s Method
o P01 = ∑P1Q0 + ∑P1Q1
∑P0Q0 ∑P0Q1 x 100
2
Marshall-Edgeworth’s Method
o P01 = ∑P1Q0 + ∑P1Q1 x 100
∑P0Q0 + ∑P0Q1
Fisher’s Method
o P01 =√ ∑P1Q0 x ∑P1Q1 x 100∑P0Q0 ∑P0Q1
Kelly’s Method
o P01 = ∑P1Q x 100
∑P0Q
Here,Q = Q0 + Q1
2
Weighted Average of Price Relative / Family Budget Method
P01 = ∑PV ∑V
Here, P = Price Relatives V = P0Q0
Components of Time Series
Secular Trend
Cyclical Variations
Seasonal Variations
Irregular or Random Variations
Methods of Measuring Trend
Free Hand Curve Method
Semi Average Method
Moving Average Method
Method of Least Square
Semi Average Method
Annual Change =
Difference of Two Semi Average Values
Difference of Years of Semi Average
Method of Least Square
o Equation for Time SeriesY = a + bX
To calculate a and b, Solve the following Equations:
∑Y = aN + b∑X
∑XY = a∑X + b∑X²
Here,
Y = Given Data i.e. Sales or Profit etc.
X= Years in terms of Units like 1,2,3 etc.