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Question 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 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 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 video game player had a relatively small variability for their middle scores. An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores.

1 answer

To determine the correct interpretation of the IQR (Interquartile Range) for the given dataset of video game scores, we first need to calculate the IQR.

  1. Order the scores: 287, 287, 290, 295, 329, 365, 387, 389, 397.

  2. Find the first quartile (Q1): This is the median of the lower half (excluding the overall median if there's an odd number of values).

    • Lower half: 287, 287, 290, 295
    • Q1 = (287 + 290) / 2 = 288.5

  3. Find the third quartile (Q3): This is the median of the upper half.

    • Upper half: 365, 387, 389, 397
    • Q3 = (387 + 389) / 2 = 388

  4. Calculate the IQR:

    • IQR = Q3 - Q1 = 388 - 288.5 = 99.5

Now we have the IQR value of 99.5, which describes the variability of the middle 50% of the scores.

Now, let’s analyze the response options:

  • An IQR of 99.5 indicates that the average score was 99.5 points. (False: IQR does not indicate average.)
  • An IQR of 329 indicates that the center of the data is around this score. (False: IQR does not indicate the center.)
  • An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (False: An IQR of 99.5 typically indicates moderate variability.)
  • An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. (False: Again IQR is 99.5, not 329.)

Conclusion: None of the provided responses are correct interpretations concerning the IQR of 99.5 in relation to the scores. The IQR suggests a moderate level of variability among the middle 50% of the scores, but none of the statements reflect this accurately.