Home > Statistical Methods calculators > Covariance - Population cov(x,y), Sample cov(x,y) for bivariate grouped data calculator

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Problem: Covariance {{50-55,55-60,60-65,65-70},{90-100,100-110,110-120,120-130},{{4,7,5,2},{6,10,7,4},{6,12,10,7},{3,8,6,3}}} [ Calculator, Method and examples ]

Solution:
Your problem -> Covariance {{50-55,55-60,60-65,65-70},{90-100,100-110,110-120,120-130},{{4,7,5,2},{6,10,7,4},{6,12,10,7},{3,8,6,3}}}

 C.I.(y) 90 - 100 100 - 110 110 - 120 120 - 130 M.V.(y) 95 105 115 125 C.I.(x) M.V.(x) dydx -1 0 1 2 f_x fdx fdx^2 fdxdy 50 - 55 52.5 -1 [4]4 [0]7 [-5]5 [-4]2 18 -18 18 -5 55 - 60 57.5 0 [0]6 [0]10 [0]7 [0]4 27 0 0 0 60 - 65 62.5 1 [-6]6 [0]12 [10]10 [14]7 35 35 35 18 65 - 70 67.5 2 [-6]3 [0]8 [12]6 [12]3 20 40 80 18 f_y 19 37 28 16 100 57 133 31 fdy -19 0 28 32 41 fdy^2 19 0 28 64 111 fdxdy -8 0 17 22 31

Population Cov(x,y) :
Population Cov(x,y) = (sum fdxdy - (sum fdx * sum fdy)/n)/(n)

=(31 - (57 xx 41)/100)/100

=(31 - (2337)/100)/100

=(31 - 23.37)/100

=(7.63)/100

=0.0763

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