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 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 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.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
. Which best describes the variability of the temperature?(1 point)
Responses
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 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.
The IQR is 17, making the temperatures easy to predict because the data values are close together.
Answers
GPT-4o mini
To determine the variability of the temperatures recorded, let's calculate the important statistics: the range and the interquartile range (IQR).
1. **Data set:** {71, 74, 81, 78, 67, 69, 64}
2. **Range:**
- The maximum temperature is 81.
- The minimum temperature is 64.
- Range = Max - Min = 81 - 64 = 17.
3. **Interquartile Range (IQR):**
- First, we need to sort the data: {64, 67, 69, 71, 74, 78, 81}.
- The median (Q2) is the middle value, which is 71.
- For Q1 (the first quartile), take the median of the first half of the data: {64, 67, 69} → Q1 = 67.
- For Q3 (the third quartile), take the median of the second half of the data: {74, 78, 81} → Q3 = 78.
- IQR = Q3 - Q1 = 78 - 67 = 11.
Now, based on this analysis:
- The **IQR is 11**, indicating the middle 50% of the recorded temperatures has a moderate spread.
- The **range is 17**, indicating a greater overall spread between the highest and lowest temperatures.
Thus, assessing the given responses:
1. **"The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days."** — This is a correct statement based on the IQR value.
2. **"The range is relatively low, indicating a low variability in the temperature."** — This is incorrect, as the range is relatively high (17).
3. **"The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading."** — While the range is high, there is no basis to assume the next reading will be as low as 47.
4. **"The IQR is 17, making the temperatures easy to predict because the data values are close together."** — This is incorrect, as the IQR is actually 11, not 17.
Therefore, the best option is:
**"The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days."**
1. **Data set:** {71, 74, 81, 78, 67, 69, 64}
2. **Range:**
- The maximum temperature is 81.
- The minimum temperature is 64.
- Range = Max - Min = 81 - 64 = 17.
3. **Interquartile Range (IQR):**
- First, we need to sort the data: {64, 67, 69, 71, 74, 78, 81}.
- The median (Q2) is the middle value, which is 71.
- For Q1 (the first quartile), take the median of the first half of the data: {64, 67, 69} → Q1 = 67.
- For Q3 (the third quartile), take the median of the second half of the data: {74, 78, 81} → Q3 = 78.
- IQR = Q3 - Q1 = 78 - 67 = 11.
Now, based on this analysis:
- The **IQR is 11**, indicating the middle 50% of the recorded temperatures has a moderate spread.
- The **range is 17**, indicating a greater overall spread between the highest and lowest temperatures.
Thus, assessing the given responses:
1. **"The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days."** — This is a correct statement based on the IQR value.
2. **"The range is relatively low, indicating a low variability in the temperature."** — This is incorrect, as the range is relatively high (17).
3. **"The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading."** — While the range is high, there is no basis to assume the next reading will be as low as 47.
4. **"The IQR is 17, making the temperatures easy to predict because the data values are close together."** — This is incorrect, as the IQR is actually 11, not 17.
Therefore, the best option is:
**"The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days."**