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 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.
Responses
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.
Answers
GPT-4o mini
To determine what the IQR (interquartile range) indicates about the dataset of the video game player's scores, let's first calculate the IQR.
1. **Organize the data**: The scores are: 287, 389, 287, 329, 295, 290, 397, 387, 365. Sorted, they are: 287, 287, 290, 295, 329, 365, 387, 389, 397.
2. **Find the quartiles**:
- The median (Q2) is the middle value, which is 329.
- The lower quartile (Q1) is the median of the first half: 287, 287, 290, 295 → Q1 = (287 + 290)/2 = 288.5.
- The upper quartile (Q3) is the median of the second half: 365, 387, 389, 397 → Q3 = (387 + 389)/2 = 388.
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 388 - 288.5 = 99.5.
Now, let's analyze the meaning of the IQR in the context of the dataset:
- The IQR measures the variability of the middle 50% of the data. An IQR of 99.5 means that there is substantial spread in the central 50% of the data.
- Therefore, the statement that corresponds to this meaning is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**
So the correct answer is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**
1. **Organize the data**: The scores are: 287, 389, 287, 329, 295, 290, 397, 387, 365. Sorted, they are: 287, 287, 290, 295, 329, 365, 387, 389, 397.
2. **Find the quartiles**:
- The median (Q2) is the middle value, which is 329.
- The lower quartile (Q1) is the median of the first half: 287, 287, 290, 295 → Q1 = (287 + 290)/2 = 288.5.
- The upper quartile (Q3) is the median of the second half: 365, 387, 389, 397 → Q3 = (387 + 389)/2 = 388.
3. **Calculate the IQR**:
- IQR = Q3 - Q1 = 388 - 288.5 = 99.5.
Now, let's analyze the meaning of the IQR in the context of the dataset:
- The IQR measures the variability of the middle 50% of the data. An IQR of 99.5 means that there is substantial spread in the central 50% of the data.
- Therefore, the statement that corresponds to this meaning is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**
So the correct answer is:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**