The mean and standard deviations of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations 21, 12 and 18 were incorrect. Find the mean and standard deviation if the incorrect observations were omitted.

Question

Philoid · Accepted Answer

Given that number of observations (n) = 100

Incorrect Mean (x̅ ) = 20

and Incorrect Standard deviation, (σ) = 3

We know that,

…(i)

∴ Incorrect sum of observations = 2000

Finding correct sum of observations, incorrect observations 21, 12 and 18 are removed

So, Correct sum of observations = Incorrect Sum – 21 – 12 – 18

= 2000 – 51

= 1949

Hence,

= 20.09

Now, Incorrect Standard Deviation (σ)

Squaring both the sides, we get

Since, 21, 12 and 18 are removed

So,

= 40900 – 441 – 144 – 324

= 40900 – 909

= 39991

Now,

Correct Standard Deviation

= 2.94

Hence, Correct Mean = 20.09

and Correct Standard Deviation = 2.94