Consider the numbers $$1$$ ,$$2$$,$$3$$, $$4$$, $$5$$, $$6$$,$$7$$ ,$$8$$, $$9$$ and $$10$$. If $$1$$ is added to each number, the variance of the numbers so obtained is

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Infinity Learn · Accepted Answer

Given numbers are $$1$$,$$2$$,$$3$$,$$4$$,$$5$$,$$6$$,$$7$$,$$8$$,$$9$$ and $$10$$ . If $$1$$ is added to each number, then observations will be $$2$$, $$3$$, $$4$$, $$5$$, $$6$$,$$7$$ ,$$8$$, $$9$$, $$10$$ and $$11$$.∴Σ$$xi=2+3+4+$$…$$+11$$         $$=102$$[$$2$$×$$2+9$$×$$1$$]$$=5$$[$$4+9$$]$$=65$$ and Σ$$xi2=22+32+42+52+$$…$$+112=12+22+32+$$…$$+112$$−$$12=11$$×$$12$$×$$236$$−$$1=505$$∴ $$V=s2=$$Σ$$xi2n$$−Σ$$xin2=50510$$−$$65102=50.5$$−$$(6.5)2=50.5$$−$$42.25=8.25$$

Consider the numbers 1 ,2,3, 4, 5, 6,7 ,8, 9 and 10. If 1 is added to each number, the variance of the numbers so obtained is

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