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

Answer:

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

Step-by-step explanation:

Given table showing the number of runs earned by two baseball players:

$\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} \sf Player\;A& \sf Player \;B\\\cline{1-2}\vphantom{\dfrac12} 2,1,3,8,2,3,4,4,1&1,4,5,1,2,4,5,5,10\\\cline{1-2}\end{array}$

The range of data is the difference between the maximum and minimum values.

The Interquartile Range (IQR) is the difference between the upper quarter (Q3) and the lower quartile (Q1).

Player A

• Range = 7
• IQR = 2.5

Player B

• Range = 9
• IQR = 3.5

Player B has a larger range and IQR than Player A, indicating Player B has more variability in the number of runs earned. Therefore, Player A is most consistent.

The best measure of variability for the data is the interquartile range (IQR) rather than the range, as it provides a more robust measure of variability and is less affected by extreme values.

In summary, Player A is most consistent, with an IQR of 2.5.