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Sagot :
Let's find the best measure of variability for the data and determine which player was more consistent by considering two commonly used measures of variability: the range and the interquartile range (IQR).
### Step-by-Step Solution:
1. Calculate the Range:
- The range is the difference between the maximum and minimum values in the data set.
- For Player A: The maximum value is 6 and the minimum value is 1. Therefore, the range is [tex]\( 6 - 1 = 5 \)[/tex].
- For Player B: The maximum value is 11 and the minimum value is 1. Therefore, the range is [tex]\( 11 - 1 = 10 \)[/tex].
2. Calculate the Interquartile Range (IQR):
- The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
- For Player A:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 3.
- Therefore, IQR for Player A is [tex]\( 3 - 2 = 1.0 \)[/tex].
- For Player B:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 5.
- Therefore, IQR for Player B is [tex]\( 5 - 2 = 3.0 \)[/tex].
3. Determine Consistency:
- A smaller IQR indicates more consistency because it shows that the middle 50% of the data points are closer to each other.
- Comparing the IQRs of both players, Player A has an IQR of 1.0, which is smaller than Player B’s IQR of 3.0. Therefore, Player A is more consistent.
Conclusion: Based on the interquartile range (IQR), Player A is the most consistent with an IQR of 1.0.
### Multiple Choice Answer:
The correct choice is:
- Player A is the most consistent, with an IQR of 1.5 .
(Note: The IQR given in the prompt is slightly different here, it should be "1.0" based on the data and actual calculations)
### Step-by-Step Solution:
1. Calculate the Range:
- The range is the difference between the maximum and minimum values in the data set.
- For Player A: The maximum value is 6 and the minimum value is 1. Therefore, the range is [tex]\( 6 - 1 = 5 \)[/tex].
- For Player B: The maximum value is 11 and the minimum value is 1. Therefore, the range is [tex]\( 11 - 1 = 10 \)[/tex].
2. Calculate the Interquartile Range (IQR):
- The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
- For Player A:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 3.
- Therefore, IQR for Player A is [tex]\( 3 - 2 = 1.0 \)[/tex].
- For Player B:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 5.
- Therefore, IQR for Player B is [tex]\( 5 - 2 = 3.0 \)[/tex].
3. Determine Consistency:
- A smaller IQR indicates more consistency because it shows that the middle 50% of the data points are closer to each other.
- Comparing the IQRs of both players, Player A has an IQR of 1.0, which is smaller than Player B’s IQR of 3.0. Therefore, Player A is more consistent.
Conclusion: Based on the interquartile range (IQR), Player A is the most consistent with an IQR of 1.0.
### Multiple Choice Answer:
The correct choice is:
- Player A is the most consistent, with an IQR of 1.5 .
(Note: The IQR given in the prompt is slightly different here, it should be "1.0" based on the data and actual calculations)
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