The average weight of all the 11 players of Real Madrid is 77 kg. If the average of first six light weight players of Real Madrid is 75 kg and that of the six heavy weight players of Real Madrid is 79 kg, find the average weight of the player which lies in the sixth position in the list of players when all the 11 players of Real Madrid are arranged in the order of increasing or decreasing weights. (In kg)

Given:

Average weight of 11 players = 77 kg

Average weight of 6 light weight players = 75 kg

Average weight of 6 heavy weight players = 79 kg

Concept used:

\(Average = {Sum\; of\; observations \over Total\; number\; of\; observations}\)

Calculation:

Let light weight players be 'x' and heavy weight players be 'y'

Let weight of 6th positioned player be 'z'

Average weight of light weight players = \( {x \over 6} × 75 = 450\) 

Average weight of heavy weight players = \( {y \over 6} × 79 = 474\)

Average weight of the player which lies in the sixth position (z)  

⇒ \(77 = {450 \;+\; z \;+\; 474 \over 11}\)

⇒ 77 × 11 = 924 + z

⇒ 847 = 924 + z

⇒ z = 924 - 847

⇒ z = 77

∴ The average weight of the player which lies in the sixth position in the list of players when all the 11 players of Real Madrid is 77.