Final answer:
The set with the greater variability is set 2, which has a standard deviation of 68°F. After converting the standard deviation of set 1 from 20°C to Fahrenheit (equating to 36°F), it's evident that 68°F is greater than 36°F.
Step-by-step explanation:
We are comparing the variability of two sets of temperature data, one measured in degrees Celsius (°C) and the other in degrees Fahrenheit (°F). The key to understanding this comparison is that one degree Celsius is equivalent to 1.8 degrees Fahrenheit when it comes to temperature differences, not absolute temperature measurements. Therefore, comparing the standard deviations of the two data sets requires a conversion.
The standard deviation of set 1 is given as 20°C. To compare it to set 2, which has a standard deviation of 68°F, we need to realize that a Celsius degree is larger than a Fahrenheit degree. Specifically, 1°C is equal to 1.8°F. If we multiply the Celsius standard deviation by this conversion factor, we get 20°C * 1.8 = 36°F. This is the standard deviation of set 1 converted into Fahrenheit degrees.
Now that both standard deviations are in the same unit, we can easily see that 68°F is greater than 36°F. Hence, the set with the greater variability is set 2, the one with the standard deviation of 68°F.