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

C) Player A is the most consistent, with an IQR of 2.5.

Explanation:

A measure of variability indicates how spread out the data is from the central tendency.

The best measure of variability in this context is the Interquartile Range (IQR), as it is less affected by extreme values or outliers, and focuses on the middle 50% of the data, which is useful for assessing consistency.

To determine which player was more consistent, calculate the IQR for each player.

Player A

Sort the data in ascending order:

• 1, 1, 2, 2, 3, 3, 4, 4, 8

Find the median (Q₂) by locating the middle value of the dataset:

• Q₂ = 3

Find the lower quartile (Q₁) by calculating the median of the lower half of the data (1, 1, 2, 2):

• (Q₁) = (2 + 1)/2 = 1.5

Find the upper quartile (Q₃) by calculating the median of the upper half of the data (3, 4, 4, 8):

• (Q₃) = (4 + 4)/2 = 4

Calculate the IQR by subtracting the lower median from the upper median:

• IQR = Q₃ - Q₁ = 4 - 1.5 = 2.5

Player B

Sort the data in ascending order:

• 1, 1, 2, 4, 4, 5, 5, 5, 10

Find the median (Q₂) by locating the middle value of the dataset:

• Q₂ = 4

Find the lower quartile (Q₁) by calculating the median of the lower half of the data (1, 1, 2, 4):

• (Q₁) = (2 + 1)/2 = 1.5

Find the upper quartile (Q₃) by calculating the median of the upper half of the data (5, 5, 5, 10):

• (Q₃) = (5 + 5)/2 = 5

Calculate the IQR by subtracting the lower median from the upper median:

• IQR = Q₃ - Q₁ = 5 - 1.5 = 3.5

Summary

Comparing the IQRs:

• Player A has an IQR of 2.5.
• Player B has an IQR of 3.5.

So, Player A is the most consistent according to the IQR measure of variability, as lower variability indicates greater consistency.