Question

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

Player A Player B
2, 1, 3, 8, 2, 3, 4, 3, 2 2, 3, 1, 4, 2, 2, 1, 4, 6


Find the best measure of variability for the data and determine which player was more consistent.
Player A is the most consistent, with an IQR of 1.5.
Player B is the most consistent, with an IQR of 2.5.
Player A is the most consistent, with a range of 7.
Player B is the most consistent, with a range of 5.

Answer 1

To determine the best measure of variability for the data, we need to consider the type of data we are dealing with. In this case, the data is numerical and discrete, so the best measure of variability would be the range or the interquartile range (IQR).

The range is the difference between the maximum and minimum values in a dataset, while the IQR is the range of the middle 50% of the data. The IQR is less sensitive to outliers than the range, so it is often a better measure of variability.

To calculate the range and IQR for each player, we first need to order the data:

Player A: 1, 2, 2, 2, 3, 3, 3, 4, 8

Player B: 1, 1, 2, 2, 2, 3, 4, 4, 6

Player A has a range of 8 - 1 = 7, and an IQR of Q3 - Q1 = 4 - 2.5 = 1.5.

Player B has a range of 6 - 1 = 5, and an IQR of Q3 - Q1 = 4 - 1.5 = 2.5.

Therefore, Player B has a higher range and a higher IQR, indicating more variability in their performance. Player A has a lower range and a lower IQR, indicating greater consistency in their performance. Therefore, the answer is: Player A is the most consistent.