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A video game player had the following scores: 287, 389, 287, 329, 295, 290, 397, 387, 365. What does the IQR indicate about this dataset?(1 point)

Responses

An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores.
An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores.

An IQR of 329 indicates that the center of the data is around this score.
An IQR of 329 indicates that the center of the data is around this score.

An IQR of 99.5 indicates that the average score was 99.5 points.
An IQR of 99.5 indicates that the average score was 99.5 points.

An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores.

1 answer

To analyze the dataset and determine the Interquartile Range (IQR), we first need to find the quartiles:

  1. Arrange the data in ascending order: 287, 287, 290, 295, 329, 365, 387, 389, 397

  2. Find the first quartile (Q1): This is the median of the first half of the data. The lower half is: 287, 287, 290, 295 (the median of this half is the average of the two middle numbers, 287 and 290): \[ Q1 = \frac{287 + 290}{2} = 288.5 \]

  3. Find the third quartile (Q3): This is the median of the second half of the data. The upper half is: 329, 365, 387, 389, 397 (the median of this half is the average of the two middle numbers, 365 and 387): \[ Q3 = \frac{365 + 387}{2} = 376 \]

  4. Calculate the IQR: \[ IQR = Q3 - Q1 = 376 - 288.5 = 87.5 \]

Given the calculated IQR of 87.5, none of the provided responses are correct regarding the interpretation of the IQR. However, if modifying the options for accuracy, the relevant interpretation could indicate that the IQR shows a certain level of variability among the middle scores, but not that it is specifically 'large' or 'small' based on the calculated IQR.

Therefore, a more fitting conclusion based on the calculated IQR can be derived from the context around topics of scores and range, highlighting that it indicates variability among the middle scores but would not specifically classify it without further comparison or context.

Given the options, a correct response based on common interpretations for IQR can be akin to:

  • An IQR indicates the variability for the middle scores, but the specifics of the variability (large vs small) would need more context.

Please double-check your options as they may not accurately reflect the findings.