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 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.

When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?

Answer 1

Comparing histograms of temperatures for two locations, the median is the preferred measure to determine which location is typically cooler. Histograms reveal skewness in data, and since the median is not influenced by extreme values, it indicates the central tendency more accurately than the mean in skewed distributions.

Step-by-step explanation:

When comparing the frequency of temperatures in two different locations using histograms, the median is a better measure of center than the mean, especially if the data is skewed. This is because the median is not affected by extreme values and gives a better sense of the 'typical' value in each location. The histograms for the two locations, Sunny Town and Desert Landing, indicate a range of temperatures across a 30-day period. For Sunny Town, the highest frequency is in the lower temperature range, while Desert Landing shows a higher frequency in the higher temperature ranges. To determine which location typically has the cooler temperature, we should compare the medians of the two distributions.

A histogram is used for continuous data and displays the shape of the data distribution, which can be symmetrical, normal, or skewed. Since temperature is a continuous variable, and the histograms likely show a skewed distribution, the median would serve best as the measure of central tendency for interpretation.