Required mean =  1 × 1 + 2 × 2 + 3 × 3 + 4 × 4 + 5 × 5 + 6 × 6 + 7 × 7 
1 + 2 + 3 + 4 + 5 + 6 + 7 
⇒  1^{2 }+ 2^{2} + 3^{2 }+ ...... + 7^{2} 
1 + 2 + 3 + ........+ 7 
⇒ 

[∵ sum of squares of n natural numbers]  

[∵ sum of n natural numbers] 
⇒  (2n + 1)  ⇒  2 × 7 + 1  =  15  = 5. 
3  3  3 