Question
A meteorologist recorded the following temperatures: {71,74,81,78,67,69,64}
. Today's temperature is 67º. If today’s temperature is included in the dataset, how does it change the interquartile range?(1 point)
The interquartile range of the new dataset is 9
. It changed by
The answer is NOT 0 or -2
. Today's temperature is 67º. If today’s temperature is included in the dataset, how does it change the interquartile range?(1 point)
The interquartile range of the new dataset is 9
. It changed by
The answer is NOT 0 or -2
Answers
GPT-4o mini
To find the interquartile range (IQR) of the dataset before and after including today's temperature of 67º, we will first calculate the IQR for the original dataset and then for the new dataset including today's temperature.
### Original Dataset:
The original temperatures are: {71, 74, 81, 78, 67, 69, 64}
1. **Sort the Dataset**:
{64, 67, 69, 71, 74, 78, 81}
2. **Find the Quartiles**:
- **Q1 (First Quartile)**: This is the median of the first half of the data. The first half is {64, 67, 69}, so Q1 is 67.
- **Q3 (Third Quartile)**: This is the median of the second half of the data. The second half is {71, 74, 78, 81}, so Q3 is (74 + 78) / 2 = 76.
3. **Calculate the IQR**:
\[
\text{IQR} = Q3 - Q1 = 76 - 67 = 9
\]
### New Dataset:
Adding today's temperature of 67º, our new dataset is: {71, 74, 81, 78, 67, 69, 64, 67}
1. **Sort the New Dataset**:
{64, 67, 67, 69, 71, 74, 78, 81}
2. **Find the Quartiles**:
- **Q1**: The first half is {64, 67, 67, 69}, so Q1 = (67 + 67) / 2 = 67.
- **Q3**: The second half is {71, 74, 78, 81}, so Q3 = (74 + 78) / 2 = 76.
3. **Calculate the New IQR**:
\[
\text{IQR} = Q3 - Q1 = 76 - 67 = 9
\]
### Conclusion:
The IQR before adding today's temperature is 9, and after adding today's temperature, the IQR remains 9.
Thus, the change in the interquartile range is:
\[
\text{Change} = \text{New IQR} - \text{Old IQR} = 9 - 9 = 0
\]
Therefore, the correct answer is that it did not change, which is 0. However, since it is mentioned that the answer is NOT 0 or -2, please clarify what is expected or if additional context is needed for the situation.
### Original Dataset:
The original temperatures are: {71, 74, 81, 78, 67, 69, 64}
1. **Sort the Dataset**:
{64, 67, 69, 71, 74, 78, 81}
2. **Find the Quartiles**:
- **Q1 (First Quartile)**: This is the median of the first half of the data. The first half is {64, 67, 69}, so Q1 is 67.
- **Q3 (Third Quartile)**: This is the median of the second half of the data. The second half is {71, 74, 78, 81}, so Q3 is (74 + 78) / 2 = 76.
3. **Calculate the IQR**:
\[
\text{IQR} = Q3 - Q1 = 76 - 67 = 9
\]
### New Dataset:
Adding today's temperature of 67º, our new dataset is: {71, 74, 81, 78, 67, 69, 64, 67}
1. **Sort the New Dataset**:
{64, 67, 67, 69, 71, 74, 78, 81}
2. **Find the Quartiles**:
- **Q1**: The first half is {64, 67, 67, 69}, so Q1 = (67 + 67) / 2 = 67.
- **Q3**: The second half is {71, 74, 78, 81}, so Q3 = (74 + 78) / 2 = 76.
3. **Calculate the New IQR**:
\[
\text{IQR} = Q3 - Q1 = 76 - 67 = 9
\]
### Conclusion:
The IQR before adding today's temperature is 9, and after adding today's temperature, the IQR remains 9.
Thus, the change in the interquartile range is:
\[
\text{Change} = \text{New IQR} - \text{Old IQR} = 9 - 9 = 0
\]
Therefore, the correct answer is that it did not change, which is 0. However, since it is mentioned that the answer is NOT 0 or -2, please clarify what is expected or if additional context is needed for the situation.