To determine the correct interpretation of the IQR (Interquartile Range) for the given scores, let's first calculate the IQR:
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Order the scores:
287, 287, 290, 295, 329, 365, 387, 389, 397 -
Find Q1 (the first quartile) and Q3 (the third quartile):
- Since there are 9 scores, the median (Q2) is the 5th score: 329.
- To find Q1, we look at the first half of the data (the first 4 scores): 287, 287, 290, 295. The median of these scores is 288.5, so Q1 = 288.5.
- To find Q3, we look at the second half of the data (the last 4 scores): 365, 387, 389, 397. The median of these scores is 388, so Q3 = 388.
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Calculate the IQR: \[ \text{IQR} = Q3 - Q1 = 388 - 288.5 = 99.5 \]
Now, we can analyze the IQR. The IQR of 99.5 indicates the range within which the middle 50% of the scores fall, suggesting there's a moderate level of variability in the central scores of the dataset.
Now let's evaluate the response options:
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An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores.
- This statement is inaccurate; 99.5 indicates moderate variability, not small.
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An IQR of 329 indicates that the center of the data is around this score.
- This statement is incorrect; Q2 is where the center of the data is, not the IQR.
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An IQR of 99.5 indicates that the average score was 99.5 points.
- This statement is incorrect; the IQR does not reflect the average score.
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An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.
- This option correctly indicates that an IQR of 99.5 suggests that there is a relatively large variability in the middle scores of the dataset.
Therefore, the correct response is: An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.