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Question:

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ..., x5 and a is equal to :

582.5

507.5

586.5

509.5

Solution:

→x=10→∑5i=1xi=50
S.D.=√∑5i=5x2i5−(x¯)2=8→∑5i=1(xi)2=109
Variance=∑5i=1(xi)2+(a)26−(∑5i=1xi/6)2=507.5