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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 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.
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 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.

1 answer

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

  1. Arrange the scores in ascending order:

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

  2. Find the median (Q2):

    • The median score (Q2) is the middle value. With 9 scores, the middle one is the 5th score:
    • Median (Q2) = 329

  3. Find the first quartile (Q1):

    • Q1 is the median of the first half of the data (the first four scores):
    • 287, 287, 290, 295
    • The median here is the average of 287 and 290:
    • Q1 = (287 + 290) / 2 = 288.5

  4. Find the third quartile (Q3):

    • Q3 is the median of the second half of the data (the last four scores):
    • 365, 387, 389, 397
    • The median here is the average of 387 and 389:
    • Q3 = (387 + 389) / 2 = 388

  5. Calculate the IQR:

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

Now, assessing what the IQR indicates about the dataset:

  • An IQR of 99.5 indicates the range of the middle 50% of the scores. It measures the spread of the central half of the data values.
  • A higher IQR would suggest a larger variability among the middle scores.

Given the options provided, the correct interpretation is:

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