To calculate the Interquartile Range (IQR) for the given scores, we first need to find the first quartile (Q1) and the third quartile (Q3).
The scores are: 287, 389, 287, 329, 295, 290, 397, 387, 365.
First, let's arrange the scores in ascending order: 287, 287, 290, 295, 329, 365, 387, 389, 397.
Next, we can determine Q1 and Q3:
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The first quartile (Q1) is the median of the first half of the data (1st half: 287, 287, 290, 295):
- Q1 = (287 + 290) / 2 = 288.5.
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The third quartile (Q3) is the median of the second half of the data (2nd half: 329, 365, 387, 389, 397):
- Q3 = (365 + 387) / 2 = 376.
Now we can calculate the IQR:
- IQR = Q3 - Q1 = 376 - 288.5 = 87.5.
Based on this calculation, the IQR is approximately 87.5, not 99.5 or 329 as mentioned in the options you've provided.
Given the interpretation of the IQR from the choices you provided, the most accurate would be:
- An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores.
However, since the IQR we found is around 87.5, none of the statements accurately reflect the calculated IQR. Therefore, if the IQR were indeed computed as 99.5, the statement would imply there was a relatively larger variability. The correct interpretation would then be that the player had a noticeable variability in their scores around the middle scores.
None of the given responses correctly reflects the calculation or the IQR derived from the dataset.