Consider the first $$10$$ positive integers. If we multiply each number by $$-1$$ and then add $$1$$ to each number, the variance of the numbers so obtained is

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Infinity Learn · Accepted Answer

The first $$10$$ positive integers are $$1$$ ,$$2$$,$$3$$,$$4$$,$$5$$,$$6$$,$$7$$,$$8$$,$$9$$ and $$10$$. On multiplying each number by $$-1$$, we get $$-1$$, $$-2$$, $$-3$$,$$4$$, $$-5$$, $$-6$$, $$-7$$, $$-8$$, $$-9$$, $$-10$$ on adding $$1$$ to each number , we $$get0$$,$$-1$$,$$-2$$,$$-3$$,$$-4$$,$$-5$$,$$-6$$,$$-7$$,$$-8$$,$$-9$$.∴ Σ$$xi=$$−$$9$$×$$102=$$−$$45$$ and Σ$$xi2=02+($$−$$1)2+($$−$$2)2+$$…$$+($$−$$9)2=9$$×$$10$$×$$196=285$$∴  S.D ,$$=28510$$−−$$45102=28510$$−$$2025100$$ $$=2850$$−$$2025100=8.25$$ Now, variance $$=($$ S.D. $$)2=8.25)2=8.25$$

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Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is

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