To determine the correct interpretation of the Interquartile Range (IQR) based on the given scores: 287, 389, 287, 329, 295, 290, 397, 387, 365, we first need to calculate the IQR.
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Order the data: 287, 287, 290, 295, 329, 365, 387, 389, 397
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Find the quartiles:
- Q1 (the first quartile): This is the median of the first half of the data. The first half is 287, 287, 290, and 295. The median here is the average of 287 and 290, which is (287 + 290) / 2 = 288.5.
- Q3 (the third quartile): This is the median of the second half of the data. The second half is 329, 365, 387, 389, and 397. The median here is 387.
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Calculate IQR: IQR = Q3 - Q1 = 387 - 288.5 = 98.5.
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Interpret the result: An IQR of 98.5 indicates that the variability of the middle 50% of scores is relatively small, as an IQR describes the spread of the central portion of the data.
Now, looking at the options provided:
- An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. (Incorrect)
- An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (Incorrect, although it states small variability correctly, the IQR is not 99.5)
- An IQR of 329 indicates that the center of the data is around this score. (Incorrect)
- An IQR of 99.5 indicates that the average score was 99.5 points. (Incorrect)
Conclusion: None of the provided statements are accurate based on the calculation of the IQR. The closest interpretation would be that the IQR indicates a relatively small variability for the middle scores, but the actual IQR is 98.5, not the given options.