Question Number 42058 by Rio Michael last updated on 17/Aug/18
$${Given}\:{that}\:\:\bar {\mathrm{x}}=\:\frac{\Sigma\mathrm{x}{i}}{{n}_{\mathrm{1}} }\:\:\:{and}\:\bar {{y}}=\:\frac{\Sigma{yi}}{{n}_{\mathrm{2}} } \\ $$$${show}\:{that}\: \\ $$$$\:\bar {\mathrm{x}}_{{c}} =\:\frac{{n}_{\mathrm{1}} \left(\bar {\mathrm{x}}\right)\:+\:{n}_{\mathrm{2}} \left(\bar {{y}}\right)}{{n}_{\mathrm{1}} +{n}_{\mathrm{2}} } \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 17/Aug/18
$${n}_{\mathrm{1}} \overset{−} {{x}}={x}_{\mathrm{1}} +{x}_{\mathrm{2}} +…+{x}_{{n}_{\mathrm{1}} } \\ $$$${n}_{\mathrm{2}} \overset{−} {{y}}={y}_{\mathrm{1}} +{y}_{\mathrm{2}} +…+{y}_{{n}_{\mathrm{2}} } \\ $$$$\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +…+{x}_{{n}_{\mathrm{1}} } +{y}_{\mathrm{1}} +{y}_{\mathrm{2}} +…{y}_{{n}_{\mathrm{2}} } }{{n}_{\mathrm{1}} +{n}_{\mathrm{2}} } \\ $$$$=\frac{{n}_{\mathrm{1}} \overset{−} {{x}}+{n}_{\mathrm{2}} \overset{−} {{y}}}{{n}_{\mathrm{1}} +{n}_{\mathrm{2}} } \\ $$