The organizers of a basketball tournament randomly selected three participating teams and recorded the height, in centimeters, of each player from the selected teams. The data they recorded is shown.
Team A: 191, 192, 189, 191, 194, 187, 192, 188, 192, 191, 189, 194
Team B: 195, 194, 186, 187, 190, 189, 190, 185, 195, 186, 194, 187
Team C: 192, 185, 189, 190, 186, 189, 193, 191, 185, 190, 189, 186
The organizers used the data to find the median for each sample and then estimated the median height of all players in the tournament. They estimated the median height of all the players to be 190 centimeters.
How far off might this estimate be?
To find out how far off the estimate of 190 centimeters might be, we first need to find the medians of each team.
Team A median: 191, 191, 192, 192, 192, 194
Median = (192 + 192) / 2 = 192
Team B median: 185, 186, 186, 187, 187, 189, 190, 190, 194, 195, 195
Median = 189
Team C median: 185, 185, 186, 186, 189, 189, 189, 190, 190, 191, 192, 193
Median = (189 + 190) / 2 = 189.5
Now, we calculate the median of all medians:
(192 + 189 + 189.5) / 3 = 190.17
Therefore, the estimate of 190 centimeters for the median height of all players in the tournament might be off by approximately 0.17 centimeters.