Answered

IDNLearn.com: Your destination for reliable and timely answers to any question. Whether it's a simple query or a complex problem, our experts have the answers you need.

Question 7 (Multiple Choice, Worth 2 points)

The table shows the number of goals made by two hockey players.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Player A & Player B \\
\hline
$2, 3, 1, 3, 2, 2, 1, 3, 6$ & $1, 4, 5, 1, 2, 4, 5, 5, 11$ \\
\hline
\end{tabular}
\][/tex]

Find the best measure of variability for the data and determine which player was more consistent.

A. Player B is the most consistent, with an IQR of 3.5.
B. Player B is the most consistent, with a range of 10.
C. Player A is the most consistent, with an IQR of 1.5.
D. Player A is the most consistent, with a range of 5.

Sagot :

GinnyAnsweridn
Let's find the best measure of variability for the data and determine which player was more consistent by considering two commonly used measures of variability: the range and the interquartile range (IQR).

### Step-by-Step Solution:

1. Calculate the Range:
- The range is the difference between the maximum and minimum values in the data set.
- For Player A: The maximum value is 6 and the minimum value is 1. Therefore, the range is [tex]\( 6 - 1 = 5 \)[/tex].
- For Player B: The maximum value is 11 and the minimum value is 1. Therefore, the range is [tex]\( 11 - 1 = 10 \)[/tex].

2. Calculate the Interquartile Range (IQR):
- The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
- For Player A:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 3.
- Therefore, IQR for Player A is [tex]\( 3 - 2 = 1.0 \)[/tex].

- For Player B:
- Q1 (the 25th percentile) is 2.
- Q3 (the 75th percentile) is 5.
- Therefore, IQR for Player B is [tex]\( 5 - 2 = 3.0 \)[/tex].

3. Determine Consistency:
- A smaller IQR indicates more consistency because it shows that the middle 50% of the data points are closer to each other.
- Comparing the IQRs of both players, Player A has an IQR of 1.0, which is smaller than Player B’s IQR of 3.0. Therefore, Player A is more consistent.

Conclusion: Based on the interquartile range (IQR), Player A is the most consistent with an IQR of 1.0.

### Multiple Choice Answer:
The correct choice is:
- Player A is the most consistent, with an IQR of 1.5 .

(Note: The IQR given in the prompt is slightly different here, it should be "1.0" based on the data and actual calculations)
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.