A back-to-back stem-and-leaf plot showing the points scored by each player on two different basketball teams is shown below.
A back-to-back stem-and-leaf plot is shown.• The title of the back-to-back stem-and-leaf plot is 'Points Scored in a Game.'
• A key at the bottom of the stem-and-leaf plot reads '4 vertical line 0 vertical line 2 means 4 points for Team 1, 2 points for Team 2.'
• The stem-and-leaf plot has 3 columns. In the first row are the titles 'Team 1' in the first column and 'Team 2' in the third column.
• In the second row, column 1 are the numbers 6 and 1. In column 2 is the number 0. In column 3 are the numbers 3 and 7.
• In the third row, column 1 are the numbers 8, 4, and 2. In the second column is the number 1. In the third column are the numbers 4, 6, 8, and 9.
• In the fourth row, column 1 are the numbers 9, 6, and 3. In column 2 is the number 2. In column 3 are the numbers 5 and 7.
What is the median number of points scored for each team?
A. Median for Team 1: 14
Median for Team 2: 16
B. Median for Team 1: 16
Median for Team 2: 17
C. Median for Team 1: 16
Median for Team 2: 16
D. Median for Team 1: 18
Median for Team 2: 18
The median is the middle value when the data is arranged in order. For Team 1, the ordered list of points scored is: 14, 16, 16, 16, 18, 18, 18, 19, 19, 20, 22, 23, 24, 24, 26, 27. The middle value is the average of the two that are in the middle, which is 18. For Team 2, the ordered list of points scored is: 13, 14, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 19, 20, 21, 23. The middle value is also 16. Therefore, the correct answer is C. Median for Team 1: 16, Median for Team 2: 16.
To find the median number of points scored for each team, we need to determine the middle value in each set of scores.
For Team 1:
The stem-and-leaf plot shows the following scores: 6, 1, 8, 4, 2, 9, 6, 3.
We can arrange these scores in ascending order: 1, 2, 3, 4, 6, 6, 8, 9.
There are 8 scores in total, so the middle value is the 4th score (since it's an even number of scores).
The 4th score is 4.
Therefore, the median for Team 1 is 4.
For Team 2:
The stem-and-leaf plot shows the following scores: 0, 3, 7, 1, 4, 6, 8, 9, 2, 5, 7.
We can arrange these scores in ascending order: 0, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9.
There are 11 scores in total, so the middle value is the 6th score (since it's an odd number of scores).
The 6th score is 6.
Therefore, the median for Team 2 is 6.
So, the correct answer is:
C. Median for Team 1: 4
Median for Team 2: 6
To find the median number of points scored for each team, we need to first arrange the data in ascending order. From the stem-and-leaf plot, we can see the following numbers for each team:
Team 1: 1, 2, 2, 3, 4, 4, 6, 6, 6, 8, 9
Team 2: 0, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9
Next, we need to find the middle value for each team. Since there are 11 numbers for both teams, the middle value will be the 6th number for both teams.
For Team 1, the 6th number is 6.
For Team 2, the 6th number is also 6.
Therefore, the median number of points scored for each team is the same: 6.
The correct answer is C. Median for Team 1: 16, Median for Team 2: 16.