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 $$get-1$$, $$-2$$, $$-3$$, $$4$$, $$-5$$, $$-6$$, $$-7$$, $$-8$$, $$-9$$, $$-10On$$ adding $$1$$ to each number, we $$get0$$, $$-1$$, $$-2$$, $$-3$$, $$-4$$, $$-5$$, $$-6$$, $$-7$$, $$-8$$, $$-9$$∴ Σxi    $$=$$−$$9$$×$$102=$$−$$45$$ and     Σ$$xi2=02+($$−$$1)2+($$−$$2)2+$$…$$+($$−$$9)2=9$$×$$10$$×$$196=285$$∴  S.D.     $$=28510$$−−$$45102=28510$$−$$2025100$$    $$=2850$$−$$2025100=8.25$$

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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