Question
A meteorologist recorded the following temperatures: {71,74,81,78,67,69,64}
. Which best describes the variability of the temperature?
The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.
The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.
The range is relatively low, indicating a low variability in the temperature.
The range is relatively low, indicating a low variability in the temperature.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.
. Which best describes the variability of the temperature?
The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.
The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.
The range is relatively low, indicating a low variability in the temperature.
The range is relatively low, indicating a low variability in the temperature.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.
Answers
GPT-4o mini
To analyze the variability of the recorded temperatures \( \{71, 74, 81, 78, 67, 69, 64\} \), let's calculate both the interquartile range (IQR) and the range.
1. **Arrange the temperatures in ascending order:**
\[
64, 67, 69, 71, 74, 78, 81
\]
2. **Calculate the quartiles:**
- The median (Q2) is the middle value:
\[
Q2 = 71
\]
- The first quartile (Q1) is the median of the first half (64, 67, 69):
\[
Q1 = 67
\]
- The third quartile (Q3) is the median of the second half (74, 78, 81):
\[
Q3 = 78
\]
3. **Calculate the IQR:**
\[
\text{IQR} = Q3 - Q1 = 78 - 67 = 11
\]
4. **Calculate the range:**
\[
\text{Range} = \text{Max} - \text{Min} = 81 - 64 = 17
\]
Now, let's analyze the descriptions provided:
- **The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.** \( \rightarrow \) This statement about the IQR is correct, but "fairly high variability" may be a subjective interpretation.
- **The range is relatively low, indicating a low variability in the temperature.** \( \rightarrow \) This statement is incorrect because the range is 17, which is not relatively low.
- **The IQR is 17, making the temperatures easy to predict because the data values are close together.** \( \rightarrow \) This statement is incorrect as the IQR is actually 11.
- **The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.** \( \rightarrow \) This statement is incorrect because the current temperatures recorded do not indicate that a reading of 47 degrees is expected.
Based on the calculations, the most accurate description is: **The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.** However, interpretations of variability may vary. The range of 17 indicates there is indeed noticeable variability in the overall temperature readings, albeit the range is not excessively high.
1. **Arrange the temperatures in ascending order:**
\[
64, 67, 69, 71, 74, 78, 81
\]
2. **Calculate the quartiles:**
- The median (Q2) is the middle value:
\[
Q2 = 71
\]
- The first quartile (Q1) is the median of the first half (64, 67, 69):
\[
Q1 = 67
\]
- The third quartile (Q3) is the median of the second half (74, 78, 81):
\[
Q3 = 78
\]
3. **Calculate the IQR:**
\[
\text{IQR} = Q3 - Q1 = 78 - 67 = 11
\]
4. **Calculate the range:**
\[
\text{Range} = \text{Max} - \text{Min} = 81 - 64 = 17
\]
Now, let's analyze the descriptions provided:
- **The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.** \( \rightarrow \) This statement about the IQR is correct, but "fairly high variability" may be a subjective interpretation.
- **The range is relatively low, indicating a low variability in the temperature.** \( \rightarrow \) This statement is incorrect because the range is 17, which is not relatively low.
- **The IQR is 17, making the temperatures easy to predict because the data values are close together.** \( \rightarrow \) This statement is incorrect as the IQR is actually 11.
- **The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.** \( \rightarrow \) This statement is incorrect because the current temperatures recorded do not indicate that a reading of 47 degrees is expected.
Based on the calculations, the most accurate description is: **The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.** However, interpretations of variability may vary. The range of 17 indicates there is indeed noticeable variability in the overall temperature readings, albeit the range is not excessively high.