Question

The mean and standard deviation of 18 observations are found to be 7 and 4 respectively. On rechecking it was found that an observation 12 was misread as 21. Calculate the correct mean and standard deviation.

Answer 1

Given that number of observations (n) = 18 

Incorrect Mean (x̅) = 7 

and Incorrect Standard deviation, (σ) = 4 

We know that,

∴ 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,

Correct Mean = \(\frac{Correct \,Sum\,of\,observations}{Total\,number\,of\,observations}\)  

= \(\frac{117}{18}\)

= 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