17th sum 17 From a frequency distribution consisting of 18 observations, the mean and - Maths - Statistics

Question

17th sum

17 From a frequency distribution consisting of 18 observations, the
mean and the standard deviation were found to be 7 and 4
respectively But on comparison with the original data, it was found
that a figure 12 was miscopied as 21 in calculations Calculate the
correct mean and standard deviation

Shruti Tyagi · Accepted Answer

Dear Student,

Mean x¯=∑xinincorrect mean=7⇒7=∑xi18⇒∑xi=18×7=126But 12 was read as 21, hence there was additional 21-12=9 addedso the currect sum is 126-9=117New Mean=11718=6
5Now Standard deviation =4variance=42=16Also variance σ2=1n∑x2-x¯216=118∑x2-7216×18=∑x2-49×18⇒∑x2=16×18+49×18⇒∑x2=65×18=1170Bow we need to subtract the additional digit addedHence new ∑x2=1170-212+122=1170-441+144=873Corrected variance σ2=1n∑corrected x2-corrected x¯2=118×873-6
52=48 5-42 25=6 25Standard deviation =σ2=6 252
5Hence correct answer are 6 5 and 2
5
Regards,