Question

The heights (in cm) of the volleyball 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 a greater average height?

Find the median of team A and team B.

Answer 1

Total number of players in each team = 7

Mean height of team A = `" Sum of the height of players of the team A"/"Total number of team A players"`

= `[ 180 + 178 + 176 + 181 + 190 + 175 + 187 ]/7`

= `1267/7`

= 181 cm

Mean height of team B = `" Sum of the height of players of the team B"/"Total number of team B players"`

= `[ 174 + 175 + 190 + 179 + 178 + 185 + 177 ]/7`

= `1258/7`

= 179.7 cm
Thus, team A has greater average height.

Median of team A:
Arranging heights in ascending order, we get
175, 176, 178, 180, 181, 187, 190
Total number of observations = n = 7 (odd)

∴ Median = `(( n + 1)/2)^"th" "Observation" = (( 7 + 1 )/2)^"th" "Observation" = 4^"th" "Observation" = 180 cm`

Median of team B:
Arranging heights in ascending order, we get
174, 175, 177, 178, 179, 185, 190
Total number of observations = n = 7 (odd)

∴ Median = `(( n + 1)/2)^"th" "Observation" = (( 7 + 1 )/2)^"th" "Observation" = 4^"th" "Observation" = 178 cm`