Final answer:
The statement about frequency distributions in a frequency polygon being measured on an interval or ratio scale is true, and the custom of ordering score categories in a frequency distribution from highest to lowest is false. Calculating the sum of squares, ΣX², for a given set of data, such as the score of 41 with a frequency of 3, is important in statistical analysis.
Step-by-step explanation:
The question at hand involves understanding the type of measurement scale used for certain types of data and the concept of a frequency polygon in representing this data. When a frequency distribution is presented in a frequency polygon, the scores can be measured either on an interval or ratio scale which are both forms of continuous data. This assertion is true because frequency polygons are used to represent quantitative data sets where the difference between data points is meaningful.
For instance, ratio scale data have a true zero point and allow for the comparison of values through ratios, such as weight or height measurements. Conversely, interval scale data, like temperature measured in Celsius or Fahrenheit, do not have a true zero but can still show meaningful differences between values.
Regarding the organization of score categories in a frequency distribution, it is actually more customary to list them from lowest to highest, not from the highest down to the lowest. Thus, this statement is false. As for the calculation of ΣX² given the table containing scores (X) and their frequencies (f), with the score of 41 and a frequency of 3, the value of ΣX² would be 41² × 3, resulting in 5043. This calculation demonstrates the sum of squares which is a fundamental component in various statistical formulas.