The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. One rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases. (i)      If wrong item is omitted (ii)     If it is replaced by 12.

Explanation

number of observations `{n}=20`

Incorrect mean `=10`

Incorrect standard deviation `=2`

`overline{{x}}=frac{1}{{n}} sum_{{i}=1}^{20} {x}_{{i}} `

`10=frac{1}{20} sum_{{i}=1}^{20} {x}_{{i}} `

`Rightarrow sum_{{i}=1}^{20} {x}_{{i}}=200`

incorrect sum of observations `=200`

Correct sum of observation `=200-8=192`

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