. The sum of the percent frequencies for all classes will always equal
a. one
b. the number of classes
c. the number of items in the study
d. 100
The Correct Answer and Explanation is:
Correct Answer: d. 100
Explanation:
When working with percent frequencies in statistics, we are expressing how often a class (or category) occurs relative to the total number of observations, in percentage form.
Percent frequency for a class is calculated by the formula: Percent Frequency=(Frequency of the classTotal number of observations)×100\text{Percent Frequency} = \left( \frac{\text{Frequency of the class}}{\text{Total number of observations}} \right) \times 100
This means that each class’s frequency is converted into a proportion of the whole and then scaled up to a percentage.
Because the percent frequency is based on the idea of proportions of the total, when we add up the percent frequencies of all classes, we are essentially summing up all portions of the entire dataset. In percentage terms, this total must always equal 100%, because the entire dataset is 100% of itself.
Let’s consider a simple example. Suppose you have a dataset with 4 classes and the frequencies for these classes are:
- Class A: 20 items
- Class B: 30 items
- Class C: 25 items
- Class D: 25 items
Total items = 20 + 30 + 25 + 25 = 100
Now calculate the percent frequencies:
- Class A: (20/100) × 100 = 20%
- Class B: (30/100) × 100 = 30%
- Class C: (25/100) × 100 = 25%
- Class D: (25/100) × 100 = 25%
Sum of percent frequencies = 20% + 30% + 25% + 25% = 100%
Why Other Choices Are Incorrect:
- a. One: The sum of relative frequencies (as decimals) equals 1, not percent frequencies.
- b. The number of classes: This refers to how many categories exist, not a measure of frequency.
- c. The number of items in the study: This is the sum of frequencies, not percent frequencies.
Thus, the sum of percent frequencies for all classes will always be 100.
