To interpret the Interquartile Range (IQR) of a dataset, we first need to understand that the IQR measures the spread of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). If the IQR is large, it indicates there is a greater variability among the middle 50% of the scores; if it is small, it indicates less variability.
Let's calculate the IQR for the given scores:
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Order the scores: 287, 287, 290, 295, 329, 365, 387, 389, 397
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Determine Q1 and Q3:
- The median (Q2) of the ordered dataset is 329 (the middle value).
- Q1 (the median of the first half) is the average of 290 and 295: \( Q1 = \frac{290 + 295}{2} = 292.5 \)
- Q3 (the median of the second half) is the average of 387 and 389: \( Q3 = \frac{387 + 389}{2} = 388 \)
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Calculate the IQR: \( IQR = Q3 - Q1 = 388 - 292.5 = 95.5 \)
It appears I made an error initially as the calculated IQR is 95.5, not 99.5 or 329. Here's what we can conclude from the calculated IQR:
- A relatively small IQR (like 95.5) indicates that the video game player had a relatively small variability for their middle scores.
The closest option based on this calculation is that the IQR indicates a smaller variability rather than a larger one, as suggested by one of the response options.
Now, looking at the provided answer choices, it appears that none of the options accurately reflects the calculated IQR. Therefore, if I had to interpret based on valid IQR knowledge:
An IQR of 95.5 (not listed) indicates that the video game player had a relatively small variability for their middle scores.
If you are looking for the most appropriate choice among the provided ones, please clarify or ensure the options are correct accordingly.
1 answer