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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.



Answer :

GinnyAnswer
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)

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