If the mean and standard deviation of $$5$$ observations $$x1$$, $$x2$$, $$x3$$, $$x4$$, $$x5$$ are $$10$$ and $$3$$ respectively, then the variance of $$6$$ observations $$x1$$,$$x2$$,…,$$x5$$ and $$-50$$ is equal to

Question

If the mean and standard deviation of $$5$$ observations $$x1$$, $$x2$$, $$x3$$, $$x4$$, $$x5$$ are $$10$$ and $$3$$ respectively, then the variance of $$6$$ observations $$x1$$,$$x2$$,…,$$x5$$ and $$-50$$ is equal to

Infinity Learn · Accepted Answer

It is given that    $$x1+x2+x3+x4+x55=10$$ and $$15$$∑$$i=15$$ $$xi2$$−$$102=32$$⇒ ∑$$i=15$$ $$xi=50$$  and   $$15$$∑$$i=15$$ $$xi2$$−$$100=9$$⇒ ∑$$i=15$$ $$xi=50$$  and   ∑$$i=15$$ $$xi2=545Required$$ variance $$=16$$∑$$i=15$$ $$xi2+($$−$$50)2$$−∑$$i=15$$ $$xi+($$−$$50)62$$                              $$=16{545+2500}$$−$$50$$−$$5062=30456=507.5$$

If the mean and standard deviation of $5$ observations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ are $10$ and $3$ respectively, then the variance of $6$ observations $x_{1}, x_{2}, \dots, x_{5}$ and $- 50$ is equal to

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If the mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3 respectively, then the variance of 6 observations x1,x2,…,x5 and -50 is equal to

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If the mean and standard deviation of $5$ observations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ are $10$ and $3$ respectively, then the variance of $6$ observations $x_{1}, x_{2}, \dots, x_{5}$ and $- 50$ is equal to