Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

Given: Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively

To find: the correct standard deviation.

As per given criteria,

Number of observations, n=100

Mean of the given observations before correction,

But we know,

Substituting the corresponding values, we get

⇒ ∑x_i=40× 100=4000

It is said two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively,

So ∑x_i=4000-30-70+3+27=3930

So the correct mean after correction is

Also given the standard deviation of the 100 observations is 10 before correction,

i.e., σ=10

But we know

Substituting the corresponding values, we get

Now taking square on both sides, we get

It is said two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, so correction is

So the correct standard deviation after correction is

σ=10.24

Hence the corrected standard deviation is 10.24.