Question

The histograms display the frequency of temperatures in two different locations in a 30-day period.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.

When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?

IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric

Answer 1

The Interquartile Range (IQR) is the preferred measure of variability for determining which location has the most consistent temperature, regardless of skewness, as it concentrates on the middle 50 percent of the data and is less affected by extreme values.

Step-by-step explanation:

When comparing the data for temperatures in Desert Landing and Flower Town to determine the location with the most consistent temperature, the best measure of variability to use would be the Interquartile Range (IQR). The IQR shows the range of the middle 50 percent of the data, effectively measuring the spread without being affected by outliers or extreme values. As the data for Desert Landing is not skewed, mentioning skewness for Desert Landing in the choice is incorrect. Therefore, to determine the location with the most consistent temperatures, we should be analyzing the IQR, regardless of the skewness in Desert Landing (symmetric) or Flower Town.

It's pertinent to understand that the range would consider the extreme values, which may not provide an accurate representation of the typical temperature data due to potential outliers. Whereas the IQR offers a more robust measure by focusing on the central portion of the data set, making it less sensitive to outliers. This is particularly useful when comparing the variability of the two locations without the influence of extreme temperature observations.