Question

The table shows the number of runs earned by two baseball players.

Player A Player B
2, 1, 3, 8, 2, 3, 4, 4, 1 1, 4, 5, 1, 2, 4, 5, 5, 10


Find the best measure of variability for the data and determine which player was more consistent.
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 2.5.
Player B is the most consistent, with an IQR of 3.5.

Answer 1

To find the best measure of variability for this data, we need to consider the spread of the data and the presence of outliers. The range and interquartile range (IQR) are both measures of variability that can be used in this case.

The range is the difference between the maximum and minimum values in a dataset. For Player A, the range is 8 - 1 = 7. For Player B, the range is 10 - 1 = 9.

The IQR is a measure of variability that gives the range of the middle 50% of the data. To find the IQR, we need to first find the median of the dataset, which is the middle value when the data is arranged in order. For Player A, the median is 3, and the quartiles are 2 and 4. Therefore, the IQR is 4 - 2 = 2. For Player B, the median is also 4, and the quartiles are 2 and 5. Therefore, the IQR is 5 - 2 = 3.

Based on these measures of variability, we can conclude that Player A is more consistent, as they have a smaller range and a smaller IQR. Therefore, Player A is the answer and the correct option is: Player A is the most consistent, with an IQR of 2.5.