Question
Here are the shoe sizes for a boy’s soccer team. Find the quartiles for the data.7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.5, 10.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 13.0, 13.5
Q1: 8.75; Q2: 9.75; Q3: 11.25
Q1: 7.5; Q2: 9.5; Q3: 13.25
Q1: 8.75; Q2: 9.5; Q3: 11.25
Q1: 9.0; Q2: 9.75; Q3: 11.0
Q1: 8.75; Q2: 9.75; Q3: 11.25
Q1: 7.5; Q2: 9.5; Q3: 13.25
Q1: 8.75; Q2: 9.5; Q3: 11.25
Q1: 9.0; Q2: 9.75; Q3: 11.0
Answers
GPT-4o mini
To find the quartiles for the given dataset of shoe sizes, we first list the values in order:
**Data (sorted)**:
7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.5, 10.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 13.0, 13.5
This dataset contains 25 values.
1. **Finding Q2 (Median)**:
- Since there are 25 numbers, the median (Q2) is the value at position (25 + 1) / 2 = 13th position.
- The 13th value in the ordered list is **9.5**.
2. **Finding Q1**:
- Q1 is the median of the first half of the data (the first 12 values).
- The first half (first 12 values): 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5
- Since there are 12 values, the median is the average of the 6th and 7th values:
- 6th value = 8.5
- 7th value = 9.0
- Q1 = (8.5 + 9.0) / 2 = **8.75**
3. **Finding Q3**:
- Q3 is the median of the second half of the data (the last 12 values).
- The second half (last 12 values): 9.5, 9.5, 10.0, 10.0, 10.5, 10.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 13.0, 13.5
- Similarly, since there are 12 values, the median is the average of the 6th and 7th values:
- 6th value = 10.5
- 7th value = 10.5
- Q3 = (10.5 + 10.5) / 2 = **10.5**
Thus, the quartiles for the dataset are:
- **Q1: 8.75**
- **Q2 (Median): 9.5**
- **Q3: 10.5**
Now we can check the provided options:
1. **Q1: 8.75; Q2: 9.75; Q3: 11.25** (Incorrect)
2. **Q1: 7.5; Q2: 9.5; Q3: 13.25** (Incorrect)
3. **Q1: 8.75; Q2: 9.5; Q3: 11.25** (Incorrect)
4. **Q1: 9.0; Q2: 9.75; Q3: 11.0** (Incorrect)
None of the provided options are correct. The correct quartiles are:
- **Q1: 8.75**
- **Q2: 9.5**
- **Q3: 10.5**
**Data (sorted)**:
7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5, 9.5, 10.0, 10.0, 10.5, 10.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 13.0, 13.5
This dataset contains 25 values.
1. **Finding Q2 (Median)**:
- Since there are 25 numbers, the median (Q2) is the value at position (25 + 1) / 2 = 13th position.
- The 13th value in the ordered list is **9.5**.
2. **Finding Q1**:
- Q1 is the median of the first half of the data (the first 12 values).
- The first half (first 12 values): 7.5, 7.5, 8.0, 8.0, 8.0, 8.5, 9.0, 9.0, 9.5, 9.5, 9.5, 9.5
- Since there are 12 values, the median is the average of the 6th and 7th values:
- 6th value = 8.5
- 7th value = 9.0
- Q1 = (8.5 + 9.0) / 2 = **8.75**
3. **Finding Q3**:
- Q3 is the median of the second half of the data (the last 12 values).
- The second half (last 12 values): 9.5, 9.5, 10.0, 10.0, 10.5, 10.5, 10.5, 11.0, 11.5, 12.0, 12.5, 12.5, 13.0, 13.5
- Similarly, since there are 12 values, the median is the average of the 6th and 7th values:
- 6th value = 10.5
- 7th value = 10.5
- Q3 = (10.5 + 10.5) / 2 = **10.5**
Thus, the quartiles for the dataset are:
- **Q1: 8.75**
- **Q2 (Median): 9.5**
- **Q3: 10.5**
Now we can check the provided options:
1. **Q1: 8.75; Q2: 9.75; Q3: 11.25** (Incorrect)
2. **Q1: 7.5; Q2: 9.5; Q3: 13.25** (Incorrect)
3. **Q1: 8.75; Q2: 9.5; Q3: 11.25** (Incorrect)
4. **Q1: 9.0; Q2: 9.75; Q3: 11.0** (Incorrect)
None of the provided options are correct. The correct quartiles are:
- **Q1: 8.75**
- **Q2: 9.5**
- **Q3: 10.5**