To assess the variability of the temperatures recorded {71, 74, 81, 78, 67, 69, 64}, we'll calculate both the range and the interquartile range (IQR).
-
Calculating the Range:
- The range is given by the maximum temperature minus the minimum temperature.
- Maximum: 81
- Minimum: 64
- Range = 81 - 64 = 17
-
Calculating the IQR:
- First, we need to organize the data in ascending order: {64, 67, 69, 71, 74, 78, 81}.
- The median (Q2) is the fourth number, which is 71.
- To find Q1 (the first quartile), take the median of the first half: {64, 67, 69}. The median of these numbers is 67.
- To find Q3 (the third quartile), take the median of the second half: {74, 78, 81}. The median of these numbers is 78.
- IQR = Q3 - Q1 = 78 - 67 = 11.
Now let's analyze the provided statements:
-
The IQR is 17, making the temperatures easy to predict because the data values are close together.
- Incorrect. The IQR is 11, not 17.
-
The range is relatively high, showing that the temperature will likely be as low as 47 degrees in the next temperature reading.
- Incorrect. The range is 17, not particularly high and does not suggest a temperature as low as 47 degrees based on the data provided.
-
The range is relatively low, indicating a low variability in the temperature.
- Incorrect. The range is 17, which does not indicate low variability.
-
The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.
- Correct. The IQR is indeed 11, which suggests that there is variability within the central half of the data.
So, the best description of the variability of the temperature is: "The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days."
1 answer