Question
Find the median, range, and interquartile range of both sets: Set 1: 65, 66, 77, 79, 81, 93, 104, 105 Set 2: 56, 1, 29, 72, 67, 59, 74, 60 Which is true about the two sets? (1 point) Responses Set 1 has a range of 40 and a median of 85. Set 1 has a range of 40 and a median of 85. Set 2 has data that is closer to its median than Set 1. Set 2 has data that is closer to its median than Set 1. Both sets have an interquartile range of 27. Both sets have an interquartile range of 27. Set 2 has a range of 74 and a median of 62. Set 2 has a range of 74 and a median of 62.
Answers
Answered by
GPT-4o mini
Let’s calculate the median, range, and interquartile range for both sets.
### Set 1: 65, 66, 77, 79, 81, 93, 104, 105
1. **Median**:
- There are 8 numbers (even), so the median is the average of the 4th and 5th values.
- 4th value = 79, 5th value = 81.
- Median = (79 + 81) / 2 = 80.
2. **Range**:
- Range = max - min = 105 - 65 = 40.
3. **Interquartile Range (IQR)**:
- Q1 (1st quartile) is the median of the first half (65, 66, 77, 79): (66 + 77) / 2 = 71.5.
- Q3 (3rd quartile) is the median of the second half (81, 93, 104, 105): (93 + 104) / 2 = 98.5.
- IQR = Q3 - Q1 = 98.5 - 71.5 = 27.
### Set 2: 56, 1, 29, 72, 67, 59, 74, 60
1. **Sort the Set**:
- Sorted: 1, 29, 56, 59, 60, 67, 72, 74.
2. **Median**:
- There are 8 numbers (even), so the median is the average of the 4th and 5th values.
- 4th value = 59, 5th value = 60.
- Median = (59 + 60) / 2 = 59.5.
3. **Range**:
- Range = max - min = 74 - 1 = 73.
4. **Interquartile Range (IQR)**:
- Q1 (1st quartile) is the median of the first half (1, 29, 56, 59): (29 + 56) / 2 = 42.5.
- Q3 (3rd quartile) is the median of the second half (60, 67, 72, 74): (67 + 72) / 2 = 69.5.
- IQR = Q3 - Q1 = 69.5 - 42.5 = 27.
### Summary of Results:
- **Set 1**: Median = 80, Range = 40, IQR = 27.
- **Set 2**: Median = 59.5, Range = 73, IQR = 27.
### Responses:
1. **Set 1 has a range of 40 and a median of 85**: False (Median is 80).
2. **Set 2 has data that is closer to its median than Set 1**: This cannot be determined solely from the median.
3. **Both sets have an interquartile range of 27**: True (Both have IQR = 27).
4. **Set 2 has a range of 74 and a median of 62**: False (Range is 73, Median is 59.5).
The correct response is:
**Both sets have an interquartile range of 27.**
### Set 1: 65, 66, 77, 79, 81, 93, 104, 105
1. **Median**:
- There are 8 numbers (even), so the median is the average of the 4th and 5th values.
- 4th value = 79, 5th value = 81.
- Median = (79 + 81) / 2 = 80.
2. **Range**:
- Range = max - min = 105 - 65 = 40.
3. **Interquartile Range (IQR)**:
- Q1 (1st quartile) is the median of the first half (65, 66, 77, 79): (66 + 77) / 2 = 71.5.
- Q3 (3rd quartile) is the median of the second half (81, 93, 104, 105): (93 + 104) / 2 = 98.5.
- IQR = Q3 - Q1 = 98.5 - 71.5 = 27.
### Set 2: 56, 1, 29, 72, 67, 59, 74, 60
1. **Sort the Set**:
- Sorted: 1, 29, 56, 59, 60, 67, 72, 74.
2. **Median**:
- There are 8 numbers (even), so the median is the average of the 4th and 5th values.
- 4th value = 59, 5th value = 60.
- Median = (59 + 60) / 2 = 59.5.
3. **Range**:
- Range = max - min = 74 - 1 = 73.
4. **Interquartile Range (IQR)**:
- Q1 (1st quartile) is the median of the first half (1, 29, 56, 59): (29 + 56) / 2 = 42.5.
- Q3 (3rd quartile) is the median of the second half (60, 67, 72, 74): (67 + 72) / 2 = 69.5.
- IQR = Q3 - Q1 = 69.5 - 42.5 = 27.
### Summary of Results:
- **Set 1**: Median = 80, Range = 40, IQR = 27.
- **Set 2**: Median = 59.5, Range = 73, IQR = 27.
### Responses:
1. **Set 1 has a range of 40 and a median of 85**: False (Median is 80).
2. **Set 2 has data that is closer to its median than Set 1**: This cannot be determined solely from the median.
3. **Both sets have an interquartile range of 27**: True (Both have IQR = 27).
4. **Set 2 has a range of 74 and a median of 62**: False (Range is 73, Median is 59.5).
The correct response is:
**Both sets have an interquartile range of 27.**
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