Question
A meteorologist recorded the following temperatures: {71,74,81,78,67,69,64}
. Which best describes the variability of the temperature?(1 point)
Responses
The range is relatively low, indicating a low variability in the temperature.
The range is relatively low, indicating a low variability in the temperature. - no response given
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading. - incorrect
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. - no response given
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. - no response given
Incorrect
. Which best describes the variability of the temperature?(1 point)
Responses
The range is relatively low, indicating a low variability in the temperature.
The range is relatively low, indicating a low variability in the temperature. - no response given
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading. - incorrect
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. - no response given
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. - no response given
Incorrect
Answers
GPT-4o mini
To analyze the variability of the recorded temperatures {71, 74, 81, 78, 67, 69, 64}, we can compute both the range and the interquartile range (IQR).
1. **Range**: The range is calculated by subtracting the minimum value from the maximum value.
- Maximum value = 81
- Minimum value = 64
- Range = 81 - 64 = 17
2. **IQR**: The IQR requires finding the first quartile (Q1) and the third quartile (Q3).
- First, we sort the data: {64, 67, 69, 71, 74, 78, 81}
- Q1 (the median of the first half) is the median of {64, 67, 69}: Q1 = 67
- Q3 (the median of the second half) is the median of {71, 74, 78, 81}: Q3 = 76
- IQR = Q3 - Q1 = 76 - 67 = 9
Given the calculations:
- The range of the temperatures is 17, which indicates a moderate level of variability.
- The IQR of the temperatures is 9, suggesting a moderate variability for the middle 50% of the recorded days.
Now let's analyze the response options based on this data:
- "The range is relatively low, indicating a low variability in the temperature." - **Incorrect** (since the range is 17, which is not low).
- "The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading." - **Incorrect** (because there's no basis for predicting 47 degrees based on the given data).
- "The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days." - **Incorrect** (the IQR is actually 9, not 11).
- "The IQR is 17, making the temperatures easy to predict because the data values are close together." - **Incorrect** (the IQR is not 17).
The most accurate conclusion based on the calculations is that the range (17) indicates moderate variability, and the IQR (9) shows variability within the central 50% of the data points. However, none of the provided statements accurately reflect these findings.
If you need to describe the variability based on the original data provided, the best statement would be something akin to: "The range is 17, indicating moderate variability in the temperature data."
1. **Range**: The range is calculated by subtracting the minimum value from the maximum value.
- Maximum value = 81
- Minimum value = 64
- Range = 81 - 64 = 17
2. **IQR**: The IQR requires finding the first quartile (Q1) and the third quartile (Q3).
- First, we sort the data: {64, 67, 69, 71, 74, 78, 81}
- Q1 (the median of the first half) is the median of {64, 67, 69}: Q1 = 67
- Q3 (the median of the second half) is the median of {71, 74, 78, 81}: Q3 = 76
- IQR = Q3 - Q1 = 76 - 67 = 9
Given the calculations:
- The range of the temperatures is 17, which indicates a moderate level of variability.
- The IQR of the temperatures is 9, suggesting a moderate variability for the middle 50% of the recorded days.
Now let's analyze the response options based on this data:
- "The range is relatively low, indicating a low variability in the temperature." - **Incorrect** (since the range is 17, which is not low).
- "The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading." - **Incorrect** (because there's no basis for predicting 47 degrees based on the given data).
- "The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days." - **Incorrect** (the IQR is actually 9, not 11).
- "The IQR is 17, making the temperatures easy to predict because the data values are close together." - **Incorrect** (the IQR is not 17).
The most accurate conclusion based on the calculations is that the range (17) indicates moderate variability, and the IQR (9) shows variability within the central 50% of the data points. However, none of the provided statements accurately reflect these findings.
If you need to describe the variability based on the original data provided, the best statement would be something akin to: "The range is 17, indicating moderate variability in the temperature data."