Q.4. The mean of 'n' observation is x ¯ , if the first term is increased by 1, second by 2 and so on. What will be the new mean?

Dear Student,


Let x1,x2,,....xn be n terms.the mean x=x1+x2+,...+xnnwhen 1 is added to x1, 2 is added to x2   and n is addeto xnwe getx1+1+x2+2+,...+xn+nx1+x2+,...+xn+1+2+3+4+....+nNow 1+2+3+4+....+n is AP with first term as 1 and common difference as 1hence sum of such AP=n2×2+n-1×1n2×n+1hence we get 1+2+3+4+....+n=n2×n+1Now new mean=x1+x2+,...+xn+1+2+3+4+....+nnx1+x2+,...+xnn+1+2+3+4+....+nnx+n+12×nnx+n+12Hence answer is x+n+12

Regards,

  • 0
What are you looking for?