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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?

Answers:
• 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 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 video game player had a relatively large variability for their middle scores.

1 answer

To determine what the IQR (Interquartile Range) indicates about the dataset, let's first calculate the IQR.

  1. Organize the Scores: Arrange the scores in ascending order:

    • 287, 287, 290, 295, 329, 365, 387, 389, 397

  2. Find the Quartiles:

    • Q1 (the first quartile) is the median of the first half of the dataset. For the scores 287, 287, 290, and 295, the median (average of 287 and 290) is: \[ Q1 = \frac{287 + 290}{2} = 288.5 \]
    • Q3 (the third quartile) is the median of the second half of the dataset. For the scores 329, 365, 387, 389, and 397, the median (average of 387 and 389) is: \[ Q3 = \frac{387 + 389}{2} = 388 \]

  3. Calculate the IQR:

    • The IQR is given by: \[ IQR = Q3 - Q1 = 388 - 288.5 = 99.5 \]

Now that we have calculated the IQR to be 99.5, let's interpret what it indicates about the dataset:

  • The IQR represents the range of the middle 50% of the data. An IQR of 99.5 indicates that there is a relatively large variability in the middle scores when compared to other datasets where the IQR would be smaller.

Given your answer options, the correct interpretation would be:

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