To analyze the data and determine which player was more consistent, let's first summarize the relevant statistical measures and subsequently compare them.
### Calculating the Range
The range is the difference between the maximum and minimum values in a dataset.
1. Player A Goals: [2, 1, 3, 8, 2, 1, 4, 3, 1]
- Maximum value: 8
- Minimum value: 1
- Range: [tex]\(8 - 1 = 7\)[/tex]
2. Player B Goals: [2, 3, 1, 3, 2, 2, 1, 3, 6]
- Maximum value: 6
- Minimum value: 1
- Range: [tex]\(6 - 1 = 5\)[/tex]
### Calculating the Interquartile Range (IQR)
The Interquartile Range (IQR) is the difference between the first quartile (25th percentile) and the third quartile (75th percentile) values in a dataset.
1. Player A Goals:
- First Quartile (Q1): 1.5 (since it is between 1 and 2)
- Third Quartile (Q3): 3.5 (since it is between 3 and 4)
- IQR: [tex]\(3.5 - 1.5 = 2.0\)[/tex]
2. Player B Goals:
- First Quartile (Q1): 2
- Third Quartile (Q3): 3
- IQR: [tex]\(3 - 2 = 1.0\)[/tex]
### Comparing Consistency
Consistency is often best measured using the IQR because it is less affected by extreme values (outliers).
- Player A:
- Range: 7
- IQR: 2.0
- Player B:
- Range: 5
- IQR: 1.0
Based on the IQR, which is a robust measure of variability, Player B has a smaller IQR (1.0) compared to Player A (2.0). Therefore, Player B's performance is more consistent.
### Conclusion
Among the options provided, the correct answers are:
- "Player B is the most consistent, with an IQR of 1.0"
This is the most accurate statement based on the computed IQR values.
