The heights (in cm) of the volley-ball players from team A and team B were recorded as :

Team A : 180, 178, 176, 181, 190, 175, 187

Team B : 174, 175, 190, 179, 178, 185, 177

Which team had the greater average height ? Find the median of team A and team B.

Total number of players in each team = 7

Mean = $\dfrac{\text{Sum of the height of players of the team A}}{\text{Number of all players of team A}}$

Mean height of team A = $\dfrac{180 + 178 + 176 + 181 + 190 + 175 + 187}{7}$

= $\dfrac{1,267}{7}$

= 181 cm

Mean = $\dfrac{\text{Sum of the height of players of the team B}}{\text{Number of all players of team B}}$

Mean height of team B = $\dfrac{174 + 175 + 190 + 179 + 178 + 185 + 177}{7}$

= $\dfrac{1,258}{7}$

= 179.7 cm

Median of team A,

On arranging the given set of data in ascending order, we get :

175, 176, 178, 180, 181, 187, 190

Number of observations, n = 7 (odd)

Median = $\Big[\dfrac{n+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{7+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{8}{2}\Big]^{th}$ term

= $4^{th}$ term

= 180 cm

Median of team B,

On arranging the given set of data in ascending order, we get :

174, 175, 177, 178, 179, 185, 190

Number of observations, n = 7 (odd)

Median = $\Big[\dfrac{n+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{7+1}{2}\Big]^{th}$ term

= $\Big[\dfrac{8}{2}\Big]^{th}$ term

= $4^{th}$ term

= 178 cm

Hence, team A has greater average height. Median of team A is 180 cm and team B is 178 cm.