The Correct Answer and Explanation is:
Based on the statistical data provided, Florida is the better choice for Vic.
Here is a detailed explanation:
To determine the best state for Vic, we must analyze both the center of the temperature distributions, which indicates typical warmth, and their variability, which indicates consistency. Vic desires warm weather with high consistency, meaning he prefers less variation in daily temperatures.
First, let’s compare the centers of the distributions using the median. The median represents the typical or middle value of the data set. Florida has a median high temperature of 76 degrees Fahrenheit, while Texas has a median of 75 degrees Fahrenheit. Both states offer similarly warm typical days, with Florida being slightly warmer on average, satisfying Vic’s preference for warmth.
The most important factor for Vic, however, is consistency, which we measure by looking at the spread or variability of the data. The best measure for this is the interquartile range (IQR), which represents the spread of the middle 50 percent of the temperatures. A smaller IQR signifies greater consistency. For Florida, the IQR is calculated as Q3 minus Q1, which is 79 – 72 = 7 degrees. For Texas, the IQR is 85 – 60 = 25 degrees. Florida’s IQR is substantially smaller than Texas’s. This indicates that half of Florida’s daily high temperatures fall within a very narrow 7 degree window, showing remarkable consistency. In contrast, the temperatures in Texas are far more spread out.
Furthermore, the overall range (Maximum – Minimum) also supports this conclusion. Florida’s temperature range is 83 – 65 = 18 degrees, while Texas has a much larger range of 100 – 55 = 45 degrees. This shows that the temperature extremes in Texas are far more dramatic.
In summary, while both states have warm median temperatures, Florida demonstrates significantly less variability. Its small interquartile range and overall range confirm that its temperatures are far more consistent, making it the ideal choice for Vic.
