Regarding frequency tables and frequency distributions, which of the following statements is true?

• A. In a frequency distribution, the sum of all frequencies $\left({\sum }_f\right)$ is always less than the total number of observations $n$.
• B. Frequency tables do not help in identifying patterns or trends in data.
• C. A frequency table summarizes data by showing the number of times each value or class occurs in a dataset.
• D. A frequency distribution only displays qualitative data and cannot be used for quantitative data.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of a frequency table. A frequency table is a way to organize data by listing each unique value or class along with the number of times it occurs (its frequency). This helps summarize the data clearly.
2. Step 2: Recall that the sum of all frequencies in a frequency distribution equals the total number of observations in the dataset. This means the sum cannot be less than the total number of observations, so the first statement is false.
3. Step 3: Recognize that frequency tables are useful tools for identifying patterns or trends in data, such as which values occur most frequently. Therefore, the statement that frequency tables do not help in identifying patterns is false.
4. Step 4: Note that frequency distributions can be used for both qualitative (categorical) and quantitative (numerical) data. Hence, the statement that frequency distributions only display qualitative data is incorrect.
5. Step 5: Conclude that the true statement is the one describing a frequency table as summarizing data by showing the number of times each value or class occurs in a dataset, which accurately reflects the purpose of frequency tables.