Q. 65.0( 1 Vote )

# The mean and stan

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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