Question

a meteorologist recorded the following temperatures: {71, 74, 81, 78, 67, 69, 64}. which best describes the variability of the temperature? (1 point)
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 iqr is 17, making the temperatures easy to predict because the data values are close together.
the iqr is 11, indicating a fairly high variability for the temperatures for half of the recorded days.

Explanation:

Step1: Sort the data

First, sort the data set \(\{71,74,81,78,67,69,64\}\) in ascending order: \(64,67,69,71,74,78,81\).

Step2: Calculate the range

The range is calculated as \(R=\text{Max}-\text{Min}\). Here, \(\text{Max} = 81\) and \(\text{Min}=64\), so \(R=81 - 64=17\).

Step3: Calculate the IQR

The median of the data set (since \(n = 7\), the median is the 4th - ordered value) is \(Q_2=71\).
The lower half of the data is \(\{64,67,69\}\), and its median \(Q_1 = 67\).
The upper half of the data is \(\{74,78,81\}\), and its median \(Q_3=78\).
The inter - quartile range \(IQR=Q_3 - Q_1=78 - 67 = 11\).

Since the range \(R = 17\) (relatively high, as it shows a large spread from the minimum to the maximum value) and \(IQR = 11\) (not extremely low, but not as large as the range).

Answer:

The IQR is 11, indicating a fairly high variability for the temperatures for half of the recorded days.