Q. 65.0( 1 Vote )

The mean and stan

Answer :

Given that number of observations (n) = 18

Incorrect Mean (x̅ ) = 7


and Incorrect Standard deviation, (σ) = 4


We know that,






…(i)


Incorrect sum of observations = 126


Finding correct sum of observations, 12 was misread as 21


So, Correct sum of observations = Incorrect Sum – 21 + 12


= 126 – 21 + 12


= 117


Hence,




= 6.5


Now, Incorrect Standard Deviation (σ)






Squaring both the sides, we get








Since, 12 was misread as 21


So,



= 1170 – 441 + 144


= 873


Now,


Correct Standard Deviation






= 2.5


Hence, Correct Mean = 6.5


and Correct Standard Deviation = 2.5


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