Question

After constructing a relative frequency distribution summarizing IQ scores of college students, what should be the sum of the relative frequencies?
A. If percentages are used, the sum should be a 100%. If proportions are used, the sum should be 1.
B. If percentages are used, the sum should be 1%. If proportions are used, the sum should be 100.
C. If percentages are used, the sum should be 0. If proportions are used, the sum should be 0.
D. If percentages are used, the sum should be 100%. If proportions are used, the sum should be 100.

Answer 1

Answer:

• Option A. If percentages are used, the sum should be a 100%. If proportions are used, the sum should be 1.

Explanation:

The relative frequency can be measured as a ratio (proportion) or as a percentage.

As a ratio, the relative frequency is the number of times that the desired outcome is observed (either theoretically or experimentally) divided by the total number of  possible outcomes (theoretically) or  observed (experimentally).

As a percentage, the relative frequency is the ratio multiplied by 100.

This shows it mathematically:

• relative frequency of event 1 = frequency of event 1 / number of events

• relative frequency of event 2 = frequency of event 2/number of events

• relative frequency of event n = freqquency of event n/number of events

• Total relative frequency = sum of of relative frequencies

                                       = sum of all (n) frequencies / number of events =

                                       = number of events / number of events = 1

As a percentage, total relative frequency = 1 × 100 = 100