To address the question of which hockey player, A or B, is more consistent in terms of their goals, we need to analyze and compare the variability of their performance.
### Step-by-Step Solution:
#### Step 1: Define the Data
- Player A’s goals: [2, 1, 3, 8, 2, 1, 4, 3, 1]
- Player B’s goals: [2, 3, 1, 3, 2, 2, 1, 3, 6]
#### Step 2: Calculate the Range for Both Players
The range is the difference between the maximum and minimum values in the dataset.
- Range for Player A:
- Maximum: 8
- Minimum: 1
- Range: [tex]\( 8 - 1 = 7 \)[/tex]
- Range for Player B:
- Maximum: 6
- Minimum: 1
- Range: [tex]\( 6 - 1 = 5 \)[/tex]
#### Step 3: Calculate the Interquartile Range (IQR) for Both Players
The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
- IQR for Player A:
- The first quartile (Q1) is the 25th percentile.
- The third quartile (Q3) is the 75th percentile.
- For Player A, Q1 ≈ 1.0 and Q3 ≈ 3.0.
- IQR: [tex]\( 3.0 - 1.0 = 2.0 \)[/tex]
- IQR for Player B:
- The first quartile (Q1) is the 25th percentile.
- The third quartile (Q3) is the 75th percentile.
- For Player B, Q1 ≈ 2.0 and Q3 ≈ 3.0.
- IQR: [tex]\( 3.0 - 2.0 = 1.0 \)[/tex]
#### Step 4: Determine Which Player is More Consistent
To determine consistency, lower variability indicates higher consistency.
- Comparison using IQR:
- Player A's IQR: 2.0
- Player B's IQR: 1.0
- Since Player B has a lower IQR, Player B is more consistent based on IQR.
- Comparison using Range:
- Player A's range: 7
- Player B's range: 5
- While the range shows that Player B has also a lower range, the IQR is generally a better measure of consistency for data with potential outliers or non-symmetrical distribution.
Hence, the most appropriate measure of variability here is the IQR, and based on the IQR:
Player B is the most consistent, with an IQR of 1.0.
