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?
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 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.
Answers
GPT-4o mini
To find the Interquartile Range (IQR) of the dataset, we first need to arrange the scores in ascending order:
287, 287, 290, 295, 329, 365, 387, 389, 397
Next, we determine the first (Q1) and third quartiles (Q3):
- **Q1** (the median of the first half of the data, which includes the scores up to and including the median of the entire dataset) is the median of the first four values: (287, 287, 290, 295). Q1 = (287 + 290) / 2 = 288.5.
- **Q3** (the median of the second half of the data) is the median of the values (329, 365, 387, 389, 397). Q3 = (387 + 389) / 2 = 388.
Now we calculate the IQR:
\[
\text{IQR} = Q3 - Q1 = 388 - 288.5 = 99.5
\]
The IQR indicates the range between the first and third quartiles, which provides a measure of variability for the middle 50% of the data.
Now, based on the IQR calculated:
- An IQR of 99.5 indicates that there is a relatively large variability for the middle scores of the dataset.
The correct interpretation from the provided options is:
**"An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores."**
287, 287, 290, 295, 329, 365, 387, 389, 397
Next, we determine the first (Q1) and third quartiles (Q3):
- **Q1** (the median of the first half of the data, which includes the scores up to and including the median of the entire dataset) is the median of the first four values: (287, 287, 290, 295). Q1 = (287 + 290) / 2 = 288.5.
- **Q3** (the median of the second half of the data) is the median of the values (329, 365, 387, 389, 397). Q3 = (387 + 389) / 2 = 388.
Now we calculate the IQR:
\[
\text{IQR} = Q3 - Q1 = 388 - 288.5 = 99.5
\]
The IQR indicates the range between the first and third quartiles, which provides a measure of variability for the middle 50% of the data.
Now, based on the IQR calculated:
- An IQR of 99.5 indicates that there is a relatively large variability for the middle scores of the dataset.
The correct interpretation from the provided options is:
**"An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores."**