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
(1 point)
Responses
Q1
: 8.75; Q2
: 9.5; Q3
: 11.25
upper Q subscript 1 : 8.75; upper Q subscript 2 : 9.5; upper Q subscript 3 : 11.25
Q1
: 7.5; Q2
: 9.5; Q3
: 13.25
upper Q subscript 1 : 7.5; upper Q subscript 2 : 9.5; upper Q subscript 3 : 13.25
Q1
: 8.75; Q2
: 9.75; Q3
: 11.25
upper Q subscript 1 : 8.75; upper Q subscript 2 : 9.75; upper Q subscript 3 : 11.25
Q1
: 9.0; Q2
: 9.75; Q3
: 11.0
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
(1 point)
Responses
Q1
: 8.75; Q2
: 9.5; Q3
: 11.25
upper Q subscript 1 : 8.75; upper Q subscript 2 : 9.5; upper Q subscript 3 : 11.25
Q1
: 7.5; Q2
: 9.5; Q3
: 13.25
upper Q subscript 1 : 7.5; upper Q subscript 2 : 9.5; upper Q subscript 3 : 13.25
Q1
: 8.75; Q2
: 9.75; Q3
: 11.25
upper Q subscript 1 : 8.75; upper Q subscript 2 : 9.75; upper Q subscript 3 : 11.25
Q1
: 9.0; Q2
: 9.75; Q3
: 11.0
Answers
GPT-4o mini
To find the quartiles of the given shoe sizes, we need to follow these steps:
1. **Sort the data** (the data is already sorted here):
```
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
```
2. **Calculate Q2 (the median)**:
Since there are 25 data points (an odd number), the median (Q2) is the middle value, which is at position \( (25+1)/2 = 13 \).
The 13th value is:
```
Q2 = 9.5
```
3. **Calculate Q1 (the first quartile)**:
Q1 is the median of the first half of the data. The first half contains the 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
```
The median of this subset (12 values, even number) is the average of the 6th and 7th values:
```
Q1 = (8.5 + 9.0) / 2 = 8.75
```
4. **Calculate Q3 (the third quartile)**:
Q3 is the median of the second half of the data. The second half contains the 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
```
The median of this subset (12 values, even number) is the average of the 6th and 7th values:
```
Q3 = (10.5 + 11.0) / 2 = 10.75
```
Putting it all together, we have:
- Q1: 8.75
- Q2: 9.5
- Q3: 10.75
Thus, the quartiles are:
- Q1: 8.75
- Q2: 9.5
- Q3: 10.75
None of the provided answer options perfectly match these calculations, though. If options are to be reviewed or corrected, please double-check the calculations.
1. **Sort the data** (the data is already sorted here):
```
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
```
2. **Calculate Q2 (the median)**:
Since there are 25 data points (an odd number), the median (Q2) is the middle value, which is at position \( (25+1)/2 = 13 \).
The 13th value is:
```
Q2 = 9.5
```
3. **Calculate Q1 (the first quartile)**:
Q1 is the median of the first half of the data. The first half contains the 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
```
The median of this subset (12 values, even number) is the average of the 6th and 7th values:
```
Q1 = (8.5 + 9.0) / 2 = 8.75
```
4. **Calculate Q3 (the third quartile)**:
Q3 is the median of the second half of the data. The second half contains the 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
```
The median of this subset (12 values, even number) is the average of the 6th and 7th values:
```
Q3 = (10.5 + 11.0) / 2 = 10.75
```
Putting it all together, we have:
- Q1: 8.75
- Q2: 9.5
- Q3: 10.75
Thus, the quartiles are:
- Q1: 8.75
- Q2: 9.5
- Q3: 10.75
None of the provided answer options perfectly match these calculations, though. If options are to be reviewed or corrected, please double-check the calculations.