To determine what the IQR indicates about the dataset, we first need to calculate the Interquartile Range (IQR).
The IQR is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset. It measures the spread of the middle 50% of the data.
Let's organize the scores in ascending order:
- Scores: 287, 287, 290, 295, 329, 365, 387, 389, 397
Next, we find Q1 and Q3:
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Q1 (First quartile): This is the median of the first half of the data. The first half here is 287, 287, 290, 295. The median of these four numbers is the average of the two middle numbers: \[ Q1 = \frac{287 + 290}{2} = \frac{577}{2} = 288.5 \]
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Q3 (Third quartile): This is the median of the second half of the data. The second half here is 329, 365, 387, 389, 397. The median of these five numbers is the middle number: \[ Q3 = 365 \]
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IQR: Now we can calculate the IQR: \[ IQR = Q3 - Q1 = 365 - 288.5 = 76.5 \]
Now, let's analyze the provided interpretations of the IQR:
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"An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores." - Incorrect, because the calculated IQR is 76.5, not 99.5.
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"An IQR of 99.5 indicates that the average score was 99.5 points." - Incorrect, the IQR does not correspond to an average or mean score.
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"An IQR of 329 indicates that the center of the data is around this score." - Incorrect, IQR does not equal a score point; it is a measure of variability.
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"An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores." - Incorrect, as we determined the IQR is actually 76.5, which suggests a moderate variability in the middle scores.
To summarize, based on our calculations, the correct interpretation is that the IQR of 76.5 suggests a moderate amount of variability in the player's middle scores, indicating that the scores are not too widely spread around the median. All the provided interpretations are incorrect with regard to the actual IQR calculated from the dataset.