Given,
Mean of x1,x2..........,x100 is 200
So, the sum of observation will be,
∑xi=100×200
Now using the sum of A.P formula in above equation as all terms are in arithmetic progression we get,
2100(x1+x100)=100×200
⇒50(2+x100)=100×200
⇒x100=398
⇒x1+99d=398
⇒d=4
Now, xi=2+(i−1)4=4i−2
So, yi=i(xi−i)=3i2−2i
Now finding mean we get,
yˉ=1001∑yi
⇒yˉ=1001∑(3i2−2i)
⇒yˉ=1001[3×6100×101×201−22100×101]
⇒yˉ=[2101×201−101]
⇒yˉ=10049.5