Final answer:
Interval and ratio data types allow for meaningful comparison of statistics due to their measurable differences and the presence (in ratio data) of a true zero point enabling ratio calculations.
Step-by-step explanation:
The types of data that allow meaningful comparison of statistics include interval data and ratio data. Interval data has a definite ordering with measurable differences, but it does not have a true zero point, meaning that ratios are not meaningful. Ratio data, on the other hand, also has a definite ordering and measurable differences, with the addition of a true zero point, allowing for the calculation of meaningful ratios.
For example, temperature measured in degrees Celsius or Fahrenheit is interval data because differences can be measured, but 0 degrees does not represent an absence of temperature. In contrast, weight is ratio data because 0 signifies no weight, and we can say that 20 kilograms is twice as much as 10 kilograms.
Ordinal data and categorical data can be used for comparison, but they are less powerful. Ordinal data can be ordered but the differences between the data points are not meaningfully measurable. Categorical (nominal) data cannot be ordered in a meaningful way and is used for classification rather than comparison.