For two data sets, each of size $$5$$, the variance are given to be $$4$$ and $$5$$ and the corresponding means are given to be $$2$$ and $$4$$, respectively. The variance of the combined data set is

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Infinity Learn · Accepted Answer

∵σ$$x2=4$$ and σ$$y2=5Also$$, x¯$$=2$$ and y¯$$=4now$$,Σ$$xi5=2$$⇒Σ$$xi=10$$;Σ$$yi=20and$$ σ$$x2=15$$Σ$$xi2$$−(x$$¯$$)2$$⇒Σ$$xi2=5(4+4)⇒Σ$$xi2=40and$$ σ$$2y=15$$Σ$$yi2$$−(y$$¯$$)2and$$ Σ$$yi2=5(5+16)⇒Σ$$yi2=105$$ combined mean, σ$$z2=110$$Σ$$xi2+$$Σ$$yi2$$−x¯$$+y$$¯$$22=110(40+105)$$−$$9=145$$−$$9010=5510=112$$

For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

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