Mean and standard deviation of $$100$$ observations were found to be $$40$$ and $$10$$, respectively. If at the time of calculation two observations were wrongly taken as $$30$$ and $$70$$ in place of $$3$$ and $$27$$ , respectively, find the correct standard deviation.

Question

Infinity Learn · Accepted Answer

∴ New mean, ∣x¯$$=100$$×$$40+3+27$$−$$30$$−$$70100=4000$$−$$70100=3930100$$                             $$=39.3$$∵ Σ$$x2=N$$σ$$2+x$$¯$$2$$∴ $$=100(100+1600)=170000$$ New,  Σ$$x2=170000$$−$$(30)2$$−$$(70)2+(3)2+(27)2=170000$$−$$900$$−$$4900+9+729=164938$$∴ New,  $$SD=$$ New Σ$$x2N$$−$$($$ New x¯$$)2=164938100$$−$$(39.3)2=1649.38$$−$$1544.49=104.89=10.24$$

Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 , respectively, find the correct standard deviation.

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