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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 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 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 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 determine which statement about the Interquartile Range (IQR) is correct, let's calculate the IQR for the given scores:

The scores provided are: 287, 389, 287, 329, 295, 290, 397, 387, 365

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

  2. Find the median (Q2): The median is the middle value in the ordered dataset. With 9 values, the median is the 5th score: Q2 = 329

  3. Find Q1 (the median of the first half): The first half of the data (up to the median) is: 287, 287, 290, 295 Q1 is the average of the 2nd and 3rd values: Q1 = (287 + 290) / 2 = 288.5

  4. Find Q3 (the median of the second half): The second half of the data (after the median) is: 365, 387, 389, 397 Q3 is the average of the 3rd and 4th values: Q3 = (387 + 389) / 2 = 388

  5. Calculate the IQR: IQR = Q3 - Q1 = 388 - 288.5 = 99.5

Now let's interpret the responses based on the calculated IQR of 99.5:

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

    • This statement is incorrect.

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

    • This statement is incorrect as well, as it incorrectly references the IQR value.

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

    • This statement is incorrect. IQR does not indicate the average score.

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

    • This is also incorrect. An IQR of 99.5 indicates a relatively large variability for their middle scores.

Therefore, none of the provided responses correctly interpret the meaning of the IQR in the context of the dataset. However, based on the definitions, the last statement is partially aligned in the sense that an IQR of 99.5 indicates some variability in the middle scores, but "small" is not correct; it should indicate "relatively large variability."