Let the 5 consecutive odd natural numbers are (x−4),(x−2),x,(x+2) and (x+4) (x−4)2+(x−2)2+x2+(x+2)2 +(x+4)2=233×5 ⇒x2+16−8x+x2+4−4x+x2+x2 +4+4x+x2+16+8x=1165 ⇒5x2+40=1165 ⇒5x2=1125 ⇒x2=225 ⇒x=15 Now, Largest number =(x+4) =15+4=19 Smallest number =(x−4) =15−4=11 ∴ Average of 2 numbers =