The numbers of runs scored per game by this year's school baseball team and softball team are listed below.
Baseball: 0, 0, 1, 1, 1, 2, 3, 4, 5, 6, 6, 7
Softball: 0, 0, 1, 2, 4, 4, 4, 5, 7
Which statement correctly uses a measure of center to compare the two teams?
Responses
The teams scored the same number of runs per game because the median is the same for both teams.
The teams scored the same number of runs per game because the median is the same for both teams.
The teams scored the same number of runs per game because the mean runs scored for each team is the same.
The teams scored the same number of runs per game because the mean runs scored for each team is the same.
The baseball team scored more runs per game than the softball team scored because the baseball team played more games than the softball team played.
The baseball team scored more runs per game than the softball team scored because the baseball team played more games than the softball team played.
The softball team scored more runs per game than the baseball team scored because the mode for the softball game is greater than the mode for the baseball team.
The teams scored the same number of runs per game because the median is the same for both teams.
The correct statement using a measure of center to compare the two teams is:
The teams scored the same number of runs per game because the median is the same for both teams.
To compare the two teams' scores per game using a measure of center, we need to calculate the median and the mean for each team.
To find the median, we arrange the scores in ascending order and find the middle value. If the number of values is even, we take the average of the two middle values.
Here are the sorted runs per game for each team:
Baseball: 0, 0, 1, 1, 1, 2, 3, 4, 5, 6, 6, 7
Softball: 0, 0, 1, 2, 4, 4, 4, 5, 7
Now let's calculate the median for each team:
Baseball median: 1
Softball median: 4
Next, to find the mean, we add up all the scores and divide by the number of games played.
Baseball mean: (0 + 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 6 + 6 + 7) / 12 = 32 / 12 ≈ 2.67
Softball mean: (0 + 0 + 1 + 2 + 4 + 4 + 4 + 5 + 7) / 9 = 27 / 9 ≈ 3
Now we can compare the measures of center:
The baseball team's median is 1, and the softball team's median is 4. This means the statement "The teams scored the same number of runs per game because the median is the same for both teams." is incorrect.
The baseball team's mean is approximately 2.67, and the softball team's mean is approximately 3. This means the statement "The teams scored the same number of runs per game because the mean runs scored for each team is the same." is also incorrect.
The statement "The baseball team scored more runs per game than the softball team scored because the baseball team played more games than the softball team played." is incorrect because we are comparing the runs per game, not the total runs.
The correct statement is "The softball team scored more runs per game than the baseball team scored because the mode for the softball game is greater than the mode for the baseball team." To determine the mode, we find the value(s) that appear most frequently. In this case, both teams have multiple modes (0 and 1 for baseball, 4 for softball), but since 4 appears more frequently for the softball team, they scored more runs per game.