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 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 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 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.

Answer 1

To determine which statement correctly interprets the Interquartile Range (IQR) for the given dataset, we first need to calculate the IQR.

1. **Organize the scores in ascending order**:
287, 287, 290, 295, 329, 365, 387, 389, 397

2. **Identify the quartiles**:
- The median (Q2) of the dataset is the middle value of the ordered list. There are 9 scores, so the median is the 5th score: **329**.
- To find the first quartile (Q1), we look at the lower half of the data:
287, 287, 290, 295 → The median of this subset is (287 + 290) / 2 = **288.5**.
- To find the third quartile (Q3), we look at the upper half of the data:
365, 387, 389, 397 → The median of this subset is (387 + 389) / 2 = **388**.

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

Now, we can interpret the IQR. The IQR is a measure of statistical dispersion and describes the variability of the middle 50% of the data.

Since the IQR is **99.5**, we find that it indicates the extent of variability of the middle scores.

The correct response would be:
**An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**