The mean of $$5$$ observations is $$4.4$$ and the variance is $$8.24$$. If three of the five observations are $$1$$, $$2$$ and $$6$$, the two values are

Question

Infinity Learn · Accepted Answer

Σ$$xi=nx$$¯$$=5$$×$$4.4=22So$$     $$1+2+6+x4+x5=22$$          $$x4+x5=13$$                           (1)   σ$$2=1n$$∣∑$$x12$$−$$1n$$∑$$xi2$$⇒∑$$xi2=n$$σ$$2+x$$¯$$2=5(8.24+19.36)=138$$.⇒ $$1+4+36+x42+x52=138x42+x52=97So$$ $$x42+13$$−$$x42=97$$⇒$$x42+169+x42$$−$$26x4=97$$⇒ $$2x42$$−$$26x4+72=0$$⇒ $$x42$$−$$13x4+36=0$$ $$x4=13$$±$$169$$−$$1442=13$$±$$52=9$$,$$4So$$ $$x5=13$$−$$x42=4$$,$$9Hence$$, the other two nembers are $$4$$ and $$9$$.

The mean of 5 observations is 4.4 and the variance is 8.24. If three of the five observations are 1, 2 and 6, the two values are

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