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 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.

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 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach 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 Sunny Town is symmetric
IQR, because Beach Town is skewed
Range, because Sunny Town is skewed
Range, because Beach Town is symmetric

Answer 1

The appropriate measure of variability when comparing consistency of temperatures between Sunny Town and Beach Town is IQR, since it is less affected by skewness and is ideal for Beach Town's skewed temperature distribution.

Step-by-step explanation:

When comparing the consistency of temperatures between Sunny Town and Beach Town, we should look at measures of variability that give us a sense of how spread out the temperatures are. Considering that Sunny Town's histogram is symmetric and Beach Town's histogram is skewed, the Interquartile Range (IQR) is more appropriate for both datasets. The IQR is less affected by skewness and outliers, making it a better choice for assessing the central tendency in skewed distributions. The range could also be considered, but it would only give us information about the extreme values, not the consistency or variability of the data.

The student's question asked for the measure of variability that could determine the location with the most consistent temperature. As Sunny Town's temperature distribution is symmetric, and Beach Town's distribution is skewed, the correct choice is IQR, because Beach Town is skewed. The IQR provides a more accurate sense of the spread of most of the data, excluding extreme outliers that might distort the perception of consistency found when using the range.