Question

Which two types of data must have equal and measurable step sizes between values?

Answer 1

The two types of data that must have equal and measurable step sizes between values are:

Interval Data: This type of data has ordered values with equal and known distances between them, but it lacks a true zero point. An example is temperature measured in Celsius or Fahrenheit. In these scales, the difference between each degree is the same (equal step size), but there is no true zero point where the quantity being measured doesn't exist (0°C or 0°F does not mean there is no temperature).

Ratio Data: Ratio data is similar to interval data in that it has equal and measurable step sizes, but it also features a true zero point. This means that the ratio of two measurements has a meaningful interpretation. Examples include height, weight, duration, and money. In these cases, 0 represents the absence of the quantity being measured (e.g., 0 meters means no length, 0 seconds means no time elapsed).

Both interval and ratio data are types of quantitative data that allow for a wide range of statistical analyses due to their equal spacing and (in the case of ratio data) absolute zero point.

Answer 2

Interval and ratio scale level data must have equal and measurable step sizes between values. Interval data has a definite ordering and measurable differences but no true zero, whereas ratio data has both measurable differences and a true zero, allowing for meaningful ratios and precise measurements.

Step-by-step explanation:

The two types of data that must have equal and measurable step sizes between values are interval scale level data and ratio scale level data. With interval scale level data, there is a definite ordering, and the differences between the data points can be measured accurately. However, unlike ratio scale level data, interval data does not have a true zero or starting point, meaning ratios between numbers on an interval scale are not meaningful.

On the other hand, ratio scale level data, which is the highest level of measurement, not only has equal intervals but also a true zero point, allowing for the calculation of ratios. It is crucial to use the appropriate level of measurement in statistical procedures since not all operations can be used with every set of data.

When graphing these types of data, it is important to choose a scale on both axes that is appropriate to display all data points while also being able to identify trends easily. The scale chosen also affects the precision of the measuring tool — the smaller the measurement increment, the more precise the tool is considered.