The average of the squares of first ten natural numbers is:

Sum of squares of first n natural Number = \(\frac{ n (n + 1) (2n + 1) }{6}\)

N = 10

Sum of squares of first 10 natural Number = \(\frac{ 10 (10 + 1) (2 × 10 + 1) }{6}\)  = 385

∴ Average of squares of first 10 natural numbers =  \(\frac{ sum \;  of \;squares }{10}\)

∴ Average of squares of first 10 natural numbers = \(\frac{ 385}{10}\) = 38.5