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? just choose the closest answer
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 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 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 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 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 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.
Answers
GPT-4o mini
To determine the correct answer regarding the Interquartile Range (IQR) from the given scores: 287, 389, 287, 329, 295, 290, 397, 387, 365, let’s calculate the IQR.
First, we need to find the first quartile (Q1) and the third quartile (Q3):
1. Sort the data: 287, 287, 290, 295, 329, 365, hallway429, 389, 397
2. Q1 (first quartile) is the median of the first half: (287, 287, 290, 295) → Q1 = (290 + 287) / 2 = 288.5
3. Q3 (third quartile) is the median of the second half: (329, 365, 387, 389, 397) → Q3 = (387 + 389) / 2 = 388
4. IQR = Q3 - Q1 = 388 - 288.5 = 99.5
An IQR of 99.5 indicates the range of the middle 50% of scores. Therefore, a larger IQR suggests a higher variability among the middle scores, while a smaller IQR would indicate lower variability.
Based on this reasoning, the most accurate statement is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**
First, we need to find the first quartile (Q1) and the third quartile (Q3):
1. Sort the data: 287, 287, 290, 295, 329, 365, hallway429, 389, 397
2. Q1 (first quartile) is the median of the first half: (287, 287, 290, 295) → Q1 = (290 + 287) / 2 = 288.5
3. Q3 (third quartile) is the median of the second half: (329, 365, 387, 389, 397) → Q3 = (387 + 389) / 2 = 388
4. IQR = Q3 - Q1 = 388 - 288.5 = 99.5
An IQR of 99.5 indicates the range of the middle 50% of scores. Therefore, a larger IQR suggests a higher variability among the middle scores, while a smaller IQR would indicate lower variability.
Based on this reasoning, the most accurate statement is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**