Question
The data set represents the heights of players on a soccer team.
5.75, 5.16, 6, 5.25, 5.5, 6.25, 5.66, 5.33, 5.33, 6, 5.75, 5.66, 5.16
What is the interquartile range of the data set?
Responses
0.585
0.585
1.09
1.09
5.6
5.6
5.875
5.75, 5.16, 6, 5.25, 5.5, 6.25, 5.66, 5.33, 5.33, 6, 5.75, 5.66, 5.16
What is the interquartile range of the data set?
Responses
0.585
0.585
1.09
1.09
5.6
5.6
5.875
Answers
Answered by
GPT-4o mini
To find the interquartile range (IQR) of the data set, we need to follow these steps:
1. **Order the data set** from smallest to largest:
- 5.16, 5.16, 5.25, 5.33, 5.33, 5.5, 5.66, 5.66, 5.75, 5.75, 6, 6, 6.25
2. **Determine the quartiles**:
- **Q1 (the first quartile)** is the median of the first half of the data.
- The first half of the data is: 5.16, 5.16, 5.25, 5.33, 5.33, 5.5
- The median of this data (Q1) is the average of the third and fourth values:
- Q1 = (5.25 + 5.33) / 2 = 5.29
- **Q3 (the third quartile)** is the median of the second half of the data.
- The second half of the data is: 5.66, 5.66, 5.75, 5.75, 6, 6.25
- The median of this data (Q3) is the average of the third and fourth values:
- Q3 = (5.75 + 5.75) / 2 = 5.75
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 5.75 - 5.29 = 0.46
However, let's double-check the calculations for quartiles:
- When ordering the data:
- Data set: 5.16, 5.16, 5.25, 5.33, 5.33, 5.5, 5.66, 5.66, 5.75, 5.75, 6, 6, 6.25 (total of 13 numbers)
- Since there are 13 numbers, the median (Q2) is the 7th number:
- Q2 = 5.66
- Q1 (the first half of the data): 5.16, 5.16, 5.25, 5.33, 5.33, 5.5 (6 numbers)
- Q1 is the average of the 3rd and 4th numbers: Q1 = (5.25 + 5.33) / 2 = 5.29
- Q3 (the second half of the data): 5.66, 5.66, 5.75, 5.75, 6, 6.25 (6 numbers)
- Q3 is the average of the 3rd and 4th numbers: Q3 = (5.75 + 5.75) / 2 = 5.75
So, the correct calculation for the IQR is indeed:
\[
IQR = Q3 - Q1 = 5.75 - 5.29 = 0.46
\]
None of the provided options match the IQR I calculated. If the IQR is calculated differently based on software or method, please verify the methodology used for the options given. Based on the calculations presented, the IQR is 0.46, which is not one of the choices listed.
1. **Order the data set** from smallest to largest:
- 5.16, 5.16, 5.25, 5.33, 5.33, 5.5, 5.66, 5.66, 5.75, 5.75, 6, 6, 6.25
2. **Determine the quartiles**:
- **Q1 (the first quartile)** is the median of the first half of the data.
- The first half of the data is: 5.16, 5.16, 5.25, 5.33, 5.33, 5.5
- The median of this data (Q1) is the average of the third and fourth values:
- Q1 = (5.25 + 5.33) / 2 = 5.29
- **Q3 (the third quartile)** is the median of the second half of the data.
- The second half of the data is: 5.66, 5.66, 5.75, 5.75, 6, 6.25
- The median of this data (Q3) is the average of the third and fourth values:
- Q3 = (5.75 + 5.75) / 2 = 5.75
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 5.75 - 5.29 = 0.46
However, let's double-check the calculations for quartiles:
- When ordering the data:
- Data set: 5.16, 5.16, 5.25, 5.33, 5.33, 5.5, 5.66, 5.66, 5.75, 5.75, 6, 6, 6.25 (total of 13 numbers)
- Since there are 13 numbers, the median (Q2) is the 7th number:
- Q2 = 5.66
- Q1 (the first half of the data): 5.16, 5.16, 5.25, 5.33, 5.33, 5.5 (6 numbers)
- Q1 is the average of the 3rd and 4th numbers: Q1 = (5.25 + 5.33) / 2 = 5.29
- Q3 (the second half of the data): 5.66, 5.66, 5.75, 5.75, 6, 6.25 (6 numbers)
- Q3 is the average of the 3rd and 4th numbers: Q3 = (5.75 + 5.75) / 2 = 5.75
So, the correct calculation for the IQR is indeed:
\[
IQR = Q3 - Q1 = 5.75 - 5.29 = 0.46
\]
None of the provided options match the IQR I calculated. If the IQR is calculated differently based on software or method, please verify the methodology used for the options given. Based on the calculations presented, the IQR is 0.46, which is not one of the choices listed.