NCERT Class 11-Math's: Exemplar Chapter –15 Statistics Part 10

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Question 22:

Mean and standard deviation of observations were found to be and , respectively. If at the time of calculation two observations were wrongly taken as and in place of and respectively, find the correct standard deviation.

Answer:

Given: Mean and standard deviation of observations were found to be and , respectively. If at the time of calculation two observations were wrongly taken as and in place of and respectively

To find: the correct standard deviation.

As per given criteria,

Number of observations,

Mean of the given observations before correction,

But we know,

Substituting the corresponding values, we get

It is said two observations were wrongly taken as and in place of and respectively,

So

So the correct mean after correction is

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

i.e.,

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 and in place of and respectively, so correction is

So the correct standard deviation after correction is

Hence the corrected standard deviation is .