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 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 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.
Responses
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 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.
Answers
Answered by
GPT-4o mini
To determine the correct response about the Interquartile Range (IQR) for the given dataset, we first need to calculate the IQR.
1. **Sort the scores:**
- Sorted scores: 287, 287, 290, 295, 329, 365, 387, 389, 397
2. **Find the first quartile (Q1):**
- Q1 is the median of the first half of the data (lower half):
- Lower half: 287, 287, 290, 295
- Median of lower half: (287 + 290) / 2 = 288.5
3. **Find the third quartile (Q3):**
- Q3 is the median of the second half of the data (upper half):
- Upper half: 329, 365, 387, 389, 397
- Median of upper half: 387
4. **Calculate IQR:**
- IQR = Q3 - Q1 = 387 - 288.5 = 98.5
Based on the calculated IQR of 98.5, we can evaluate the given options. The values provided in the responses regarding the IQR of "99.5" seem incorrect as per calculations.
As for interpretations:
- **An IQR of 99.5 indicates that the average score was 99.5 points. (Incorrect)**
- **An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. (Incorrect)**
- **An IQR of 329 indicates that the center of the data is around this score. (Incorrect)**
- **An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (Correct in context, as 98.5 indicates small variability, but this number is also inaccurate).**
The closest correct interpretation is that the IQR indicates variability (and indeed if it were 99.5, it would indicate a relatively smaller spread of middle scores), but since the actual calculation doesn't match the given options, the responses seem to have some errors.
**In conclusion, none of the provided statements are accurate. The correct interpretation of the IQR we calculated (98.5) would indicate that the player had relatively small variability in their middle scores around the central majority of their data.**
1. **Sort the scores:**
- Sorted scores: 287, 287, 290, 295, 329, 365, 387, 389, 397
2. **Find the first quartile (Q1):**
- Q1 is the median of the first half of the data (lower half):
- Lower half: 287, 287, 290, 295
- Median of lower half: (287 + 290) / 2 = 288.5
3. **Find the third quartile (Q3):**
- Q3 is the median of the second half of the data (upper half):
- Upper half: 329, 365, 387, 389, 397
- Median of upper half: 387
4. **Calculate IQR:**
- IQR = Q3 - Q1 = 387 - 288.5 = 98.5
Based on the calculated IQR of 98.5, we can evaluate the given options. The values provided in the responses regarding the IQR of "99.5" seem incorrect as per calculations.
As for interpretations:
- **An IQR of 99.5 indicates that the average score was 99.5 points. (Incorrect)**
- **An IQR of 329 indicates that the video game player had a relatively large variability for their middle scores. (Incorrect)**
- **An IQR of 329 indicates that the center of the data is around this score. (Incorrect)**
- **An IQR of 99.5 indicates that the video game player had a relatively small variability for their middle scores. (Correct in context, as 98.5 indicates small variability, but this number is also inaccurate).**
The closest correct interpretation is that the IQR indicates variability (and indeed if it were 99.5, it would indicate a relatively smaller spread of middle scores), but since the actual calculation doesn't match the given options, the responses seem to have some errors.
**In conclusion, none of the provided statements are accurate. The correct interpretation of the IQR we calculated (98.5) would indicate that the player had relatively small variability in their middle scores around the central majority of their data.**
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