Question
The table shows the total number of students who participate in spirit week each day at a high school.
Day Students
Monday
Tuesday
Wednesday ?
Thursday
Friday
If a median of 70 students participate in spirit week each day, which could be the total number of students who participate in spirit week on Wednesday?
Responses
students
70 students
students
75 students
students
80 students
students
Day Students
Monday
Tuesday
Wednesday ?
Thursday
Friday
If a median of 70 students participate in spirit week each day, which could be the total number of students who participate in spirit week on Wednesday?
Responses
students
70 students
students
75 students
students
80 students
students
Answers
GPT-4o mini
To find the possible number of students who participate on Wednesday while keeping the median at 70, we first need to understand how the median works in a data set.
In a set of numbers, the median is the middle value when the numbers are arranged in ascending order. In this case, since we assume there are five days (Monday, Tuesday, Wednesday, Thursday, and Friday), the median will be the third value in the sorted list of participation numbers.
Since we know the median is 70, this means that when we arrange the number of students from the five days in order, the third value must be 70.
Let's consider the options provided for Wednesday:
1. **If Wednesday is 70**:
- For the median to remain 70, two days must have values equal to or less than 70, and two days must have values equal to or greater than 70.
- This is valid.
2. **If Wednesday is 75**:
- The arrangement of numbers could be something like:
- x (Monday) <= 70
- y (Tuesday) <= 70
- 75 (Wednesday)
- z (Thursday) >= 70
- w (Friday) >= 75
- In this case, to maintain a median of 70, it is still possible as we could consider having x and y both as 70 or lower.
3. **If Wednesday is 80**:
- The arrangement could be:
- x (Monday) <= 70
- y (Tuesday) <= 70
- 80 (Wednesday)
- z (Thursday) >= 70
- w (Friday) >= 80
- Here, since there would have to be at least two values below 80, it is still possible to maintain a median of 70.
From the options provided, **70, 75, and 80** each could allow for a median of 70 depending on the values of the other days.
Thus, the total number of students who participate in spirit week on Wednesday that would keep the median at 70 could be:
- **70 students**
- **75 students**
- **80 students**
All three of these options are possible.
In a set of numbers, the median is the middle value when the numbers are arranged in ascending order. In this case, since we assume there are five days (Monday, Tuesday, Wednesday, Thursday, and Friday), the median will be the third value in the sorted list of participation numbers.
Since we know the median is 70, this means that when we arrange the number of students from the five days in order, the third value must be 70.
Let's consider the options provided for Wednesday:
1. **If Wednesday is 70**:
- For the median to remain 70, two days must have values equal to or less than 70, and two days must have values equal to or greater than 70.
- This is valid.
2. **If Wednesday is 75**:
- The arrangement of numbers could be something like:
- x (Monday) <= 70
- y (Tuesday) <= 70
- 75 (Wednesday)
- z (Thursday) >= 70
- w (Friday) >= 75
- In this case, to maintain a median of 70, it is still possible as we could consider having x and y both as 70 or lower.
3. **If Wednesday is 80**:
- The arrangement could be:
- x (Monday) <= 70
- y (Tuesday) <= 70
- 80 (Wednesday)
- z (Thursday) >= 70
- w (Friday) >= 80
- Here, since there would have to be at least two values below 80, it is still possible to maintain a median of 70.
From the options provided, **70, 75, and 80** each could allow for a median of 70 depending on the values of the other days.
Thus, the total number of students who participate in spirit week on Wednesday that would keep the median at 70 could be:
- **70 students**
- **75 students**
- **80 students**
All three of these options are possible.