Question
The given dot plot shows the number of vacations taken by the sixth-grade students at Walker Junior High during one year.
plotted 0-6
0 has 3
1 has 5
2 has 7
3 has 6
4 has 4
5 has 3
6 has 1
What is the median number of vacations taken?
A.
3
B.
2
C.
7
D.
6
plotted 0-6
0 has 3
1 has 5
2 has 7
3 has 6
4 has 4
5 has 3
6 has 1
What is the median number of vacations taken?
A.
3
B.
2
C.
7
D.
6
Answers
GPT-4o mini
To find the median number of vacations taken by the sixth-grade students, we first need to list out the number of vacations taken based on the dot plot:
- 0 vacations: 3 students
- 1 vacation: 5 students
- 2 vacations: 7 students
- 3 vacations: 6 students
- 4 vacations: 4 students
- 5 vacations: 3 students
- 6 vacations: 1 student
Now, we can list all the students and their number of vacations:
- 3 students with 0 vacations: 0, 0, 0
- 5 students with 1 vacation: 1, 1, 1, 1, 1
- 7 students with 2 vacations: 2, 2, 2, 2, 2, 2, 2
- 6 students with 3 vacations: 3, 3, 3, 3, 3, 3
- 4 students with 4 vacations: 4, 4, 4, 4
- 3 students with 5 vacations: 5, 5, 5
- 1 student with 6 vacations: 6
Now, combining them gives us the ordered list:
0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6
Next, we count the total number of students:
- 3 (0s) + 5 (1s) + 7 (2s) + 6 (3s) + 4 (4s) + 3 (5s) + 1 (6) = 29 students
Since there are 29 students (an odd number), the median will be the middle number. To find the middle number, we can use the formula for the median position, which is (n + 1) / 2, where n is the number of observations.
Calculating this gives:
(29 + 1) / 2 = 30 / 2 = 15
The 15th number in the ordered list is the median.
Counting through the list we have:
1. 0
2. 0
3. 0
4. 1
5. 1
6. 1
7. 1
8. 1
9. 2
10. 2
11. 2
12. 2
13. 2
14. 2
15. 2 <- This is the 15th number in the list.
Therefore, the median number of vacations taken by the students is **2**.
The correct answer is **B. 2**.
- 0 vacations: 3 students
- 1 vacation: 5 students
- 2 vacations: 7 students
- 3 vacations: 6 students
- 4 vacations: 4 students
- 5 vacations: 3 students
- 6 vacations: 1 student
Now, we can list all the students and their number of vacations:
- 3 students with 0 vacations: 0, 0, 0
- 5 students with 1 vacation: 1, 1, 1, 1, 1
- 7 students with 2 vacations: 2, 2, 2, 2, 2, 2, 2
- 6 students with 3 vacations: 3, 3, 3, 3, 3, 3
- 4 students with 4 vacations: 4, 4, 4, 4
- 3 students with 5 vacations: 5, 5, 5
- 1 student with 6 vacations: 6
Now, combining them gives us the ordered list:
0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6
Next, we count the total number of students:
- 3 (0s) + 5 (1s) + 7 (2s) + 6 (3s) + 4 (4s) + 3 (5s) + 1 (6) = 29 students
Since there are 29 students (an odd number), the median will be the middle number. To find the middle number, we can use the formula for the median position, which is (n + 1) / 2, where n is the number of observations.
Calculating this gives:
(29 + 1) / 2 = 30 / 2 = 15
The 15th number in the ordered list is the median.
Counting through the list we have:
1. 0
2. 0
3. 0
4. 1
5. 1
6. 1
7. 1
8. 1
9. 2
10. 2
11. 2
12. 2
13. 2
14. 2
15. 2 <- This is the 15th number in the list.
Therefore, the median number of vacations taken by the students is **2**.
The correct answer is **B. 2**.