Question
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 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.
Set 1 has a range of 40 and a median of 85.
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 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.
Set 1 has a range of 40 and a median of 85.
Answers
GPT-4o mini
Let's calculate the median, range, and interquartile range for both sets of data.
### Set 1: 65, 66, 77, 79, 81, 93, 104, 105
1. **Median**:
- There are 8 numbers in this set (even number).
- To find the median, take the average of the two middle numbers.
- Middle numbers: 79 and 81.
- Median = (79 + 81) / 2 = 80.
2. **Range**:
- Range = max - min = 105 - 65 = 40.
3. **Interquartile Range (IQR)**:
- First, find the quartiles.
- Q1 (lower quartile) is the median of the first half (65, 66, 77, 79), which is (66 + 77) / 2 = 71.5.
- Q3 (upper quartile) is the median of the second half (81, 93, 104, 105), which is (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 data**: 1, 29, 56, 59, 60, 67, 72, 74
2. **Median**:
- There are 8 numbers in this set (even number).
- Middle numbers: 59 and 60.
- Median = (59 + 60) / 2 = 59.5.
3. **Range**:
- Range = max - min = 74 - 1 = 73.
4. **Interquartile Range (IQR)**:
- Q1 (lower quartile): median of (1, 29, 56, 59) = (29 + 56) / 2 = 42.5.
- Q3 (upper quartile): median of (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.
### Now, let's evaluate the provided statements:
1. **Set 2 has data that is closer to its median than Set 1.**
- This cannot be easily confirmed without calculating the distance of each point from the median.
2. **Both sets have an interquartile range of 27.**
- True, both have an IQR of 27.
3. **Set 2 has a range of 74 and a median of 62.**
- False, the range is 73 and the median is 59.5.
4. **Set 1 has a range of 40 and a median of 85.**
- False, the median is 80 (not 85), but the range is correct.
### Correct Statement:
- **Both sets have an interquartile range of 27.**
### Set 1: 65, 66, 77, 79, 81, 93, 104, 105
1. **Median**:
- There are 8 numbers in this set (even number).
- To find the median, take the average of the two middle numbers.
- Middle numbers: 79 and 81.
- Median = (79 + 81) / 2 = 80.
2. **Range**:
- Range = max - min = 105 - 65 = 40.
3. **Interquartile Range (IQR)**:
- First, find the quartiles.
- Q1 (lower quartile) is the median of the first half (65, 66, 77, 79), which is (66 + 77) / 2 = 71.5.
- Q3 (upper quartile) is the median of the second half (81, 93, 104, 105), which is (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 data**: 1, 29, 56, 59, 60, 67, 72, 74
2. **Median**:
- There are 8 numbers in this set (even number).
- Middle numbers: 59 and 60.
- Median = (59 + 60) / 2 = 59.5.
3. **Range**:
- Range = max - min = 74 - 1 = 73.
4. **Interquartile Range (IQR)**:
- Q1 (lower quartile): median of (1, 29, 56, 59) = (29 + 56) / 2 = 42.5.
- Q3 (upper quartile): median of (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.
### Now, let's evaluate the provided statements:
1. **Set 2 has data that is closer to its median than Set 1.**
- This cannot be easily confirmed without calculating the distance of each point from the median.
2. **Both sets have an interquartile range of 27.**
- True, both have an IQR of 27.
3. **Set 2 has a range of 74 and a median of 62.**
- False, the range is 73 and the median is 59.5.
4. **Set 1 has a range of 40 and a median of 85.**
- False, the median is 80 (not 85), but the range is correct.
### Correct Statement:
- **Both sets have an interquartile range of 27.**