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 .