Correct mean and CV

For a group of 100 students, the mean and coefficient of variation of their marks were found to be 60 and 25, respectively. Later, it was found that the scores 45 and 70 were wrongly entered as 40 and 27. Find the corrected mean and coefficient of variation.

Correct answer:

m =  60.48
C =  2.4445

Step-by-step explanation:

m1=60 C1=25 n=100  C = mσ m = σ/C   m =  nΣ a   m=nn m14027+45+70=100100 604027+45+70=60.48
σ1=m1 C1=60 25=1500 r1=σ12=15002=2250000  r1 = Σ (am1)2  a=m1+r1/n=60+2250000/100=75  r2=r1(40m1)2(27m1)2=2250000(4060)2(2760)2=2248511  b=m1+r2/(n2)=60+2248511/(1002)75.3011  r3=(n2) (bm)2+(45m)2+(70m)2=(1002) (75.301160.48)2+(4560.48)2+(7060.48)221857.3064  σ=r3=21857.3064147.8422  C=mσ=60.48147.8422=2.4445



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