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)

Question

Responses

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 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 99.5 indicates that the video game player had a relatively small variability for their middle scores.

Answer 1

To find the interquartile range (IQR) of the given scores, we first need to arrange the scores in ascending order:

• 287
• 287
• 290
• 295
• 329
• 365
• 387
• 389
• 397

Next, we identify the first (Q1) and third (Q3) quartiles:

• Q1 (the median of the first half of the data) is the average of 287 and 290, which equals 288.5.
• Q3 (the median of the second half of the data) is the average of 387 and 389, which equals 388.

Now, we can calculate the IQR:

• IQR = Q3 - Q1 = 388 - 288.5 = 99.5.

Based on this calculation, the IQR indicates that the range of the middle 50% of the scores is 99.5 points.

Now, looking at the response options:

1. "An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores."
2. "An IQR of 99.5 indicates that the average score was 99.5 points."
3. "An IQR of 329 indicates that the center of the data is around this score."
4. "An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores."

The correct interpretation is that an IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores.

So, the fourth option is the most accurate, as it indicates the player had a level of variability that reflects the dispersion of the middle 50% of scores rather than an average of scores.