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?

Answers:
• 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 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.

Answer 1

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

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

2. **Find the Quartiles**:
- *Q1* (the first quartile) is the median of the first half of the dataset. For the scores 287, 287, 290, and 295, the median (average of 287 and 290) is:
\[
Q1 = \frac{287 + 290}{2} = 288.5
\]
- *Q3* (the third quartile) is the median of the second half of the dataset. For the scores 329, 365, 387, 389, and 397, the median (average of 387 and 389) is:
\[
Q3 = \frac{387 + 389}{2} = 388
\]

3. **Calculate the IQR**:
- The IQR is given by:
\[
IQR = Q3 - Q1 = 388 - 288.5 = 99.5
\]

Now that we have calculated the IQR to be 99.5, let's interpret what it indicates about the dataset:

- The IQR represents the range of the middle 50% of the data. An IQR of 99.5 indicates that there is a relatively large variability in the middle scores when compared to other datasets where the IQR would be smaller.

Given your answer options, the correct interpretation would be:
- **An IQR of 99.5 indicates that the video game player had a relatively large variability for their middle scores.**