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)
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 video game player had a relatively large variability for their middle scores.
• An IQR of 329 indicates that the center of the data is around this score.

Answer 1

To find the Interquartile Range (IQR), we first need to calculate the first quartile (Q1) and the third quartile (Q3) from the dataset.

The given scores are: 287, 389, 287, 329, 295, 290, 397, 387, 365.

1. **Sort the scores:**
287, 287, 290, 295, 329, 365, 387, 389, 397

2. **Calculate Q1 (the median of the first half):**
The first half of the sorted data is: 287, 287, 290, 295
Q1 = (287 + 290) / 2 = 288.5

3. **Calculate Q3 (the median of the second half):**
The second half of the sorted data is: 329, 365, 387, 389, 397
Q3 = (387 + 389) / 2 = 388

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

Now let's assess the statements provided:

1. **An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores.**
- This statement is **incorrect**. An IQR of 99.5 indicates relatively large variability in the middle 50% of the data.

2. **An IQR of 99.5 indicates that the average score was 99.5 points.**
- This statement is **incorrect**. The IQR does not represent the average score; it represents the spread of the middle 50% of the data.

3. **An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores.**
- This statement is **incorrect** because the IQR is actually 99.5, not 329.

4. **An IQR of 329 indicates that the center of the data is around this score.**
- This statement is **incorrect**. Again, the IQR is 99.5, not 329, and the IQR does not indicate where the center of the dataset lies; it indicates the variability.

Therefore, the correct interpretation is that an IQR of 99.5 indicates relatively large variability for the middle scores. However, none of the statements provided are completely accurately reflecting the correct interpretation of the IQR.