Answer:To find the best measure of variability for the data and determine which player was more consistent, we can calculate the range and the interquartile range (IQR) for both players.
The range is calculated by subtracting the minimum value from the maximum value in a dataset. The IQR is a measure of dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset.
Let's calculate the range and IQR for both players:
For Player A:
The data for Player A is: 2, 1, 3, 8, 2, 3, 4, 4, 1.
To calculate the range:
The maximum value is 8, and the minimum value is 1.
For Player B:
The data for Player B is: 1, 4, 5, 1, 2, 4, 5, 5, 10.
To calculate the range:
The maximum value is 10, and the minimum value is 1.
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3) for each player:
For Player A:
Arranging the data in ascending order: 1, 1, 2, 2, 3, 3, 4, 4, 8.
To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 2, 3.
Q1 = 2
To calculate Q3, we find the median of the upper half of the data: 3, 4, 4, 8.
Q3 = 4
The IQR is calculated as:
For Player B:
Arranging the data in ascending order: 1, 1, 2, 4, 5, 5, 5, 10.
To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 4.
Q1 = 1.5
To calculate Q3, we find the median of the upper half of the data: 5, 5, 5, 10.
Q3 = 5
The IQR is calculated as:
Based on the calculations, we can conclude:
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 9.
Player A is the most consistent, with an IQR of 2.
Player B is the most consistent, with an IQR of 3.5.
Therefore, the correct answer is:
Player A is the most consistent, with an IQR of 2.
♥️ To find the best measure of variability for the data and determine which player was more consistent, we can calculate the range and the interquartile range (IQR) for both players.
The range is calculated by subtracting the minimum value from the maximum value in a dataset. The IQR is a measure of dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset.
Let's calculate the range and IQR for both players:
For Player A:
The data for Player A is: 2, 1, 3, 8, 2, 3, 4, 4, 1.
To calculate the range:
The maximum value is 8, and the minimum value is 1.
For Player B:
The data for Player B is: 1, 4, 5, 1, 2, 4, 5, 5, 10.
To calculate the range:
The maximum value is 10, and the minimum value is 1.
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3) for each player:
For Player A:
Arranging the data in ascending order: 1, 1, 2, 2, 3, 3, 4, 4, 8.
To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 2, 3.
Q1 = 2
To calculate Q3, we find the median of the upper half of the data: 3, 4, 4, 8.
Q3 = 4
The IQR is calculated as:
For Player B:
Arranging the data in ascending order: 1, 1, 2, 4, 5, 5, 5, 10.
To calculate Q1, we find the median of the lower half of the data: 1, 1, 2, 4.
Q1 = 1.5
To calculate Q3, we find the median of the upper half of the data: 5, 5, 5, 10.
Q3 = 5
The IQR is calculated as:
Based on the calculations, we can conclude:
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 9.
Player A is the most consistent, with an IQR of 2.
Player B is the most consistent, with an IQR of 3.5.
Therefore, the correct answer is:
Player A is the most consistent, with an IQR of 2.
♥️
Explanation: