In basic statistics and data analysis, what does it mean to calculate frequencies within a dataset?

Introduction / Context:
Frequencies are a core concept in descriptive statistics and data analysis. When you calculate frequencies, you are trying to understand how often certain values or categories appear in a dataset. This is often shown in frequency tables, bar charts or histograms and is usually one of the first steps in data exploration.

Given Data / Assumptions:
- We have a dataset consisting of multiple observations or cases.
- Each observation belongs to some category or has a certain value on a variable (for example, age group, test score range, or survey response).
- We want to understand what calculating frequencies actually means in this context.

Concept / Approach:
Calculating frequencies means counting the number of occurrences of each distinct value or category of a variable. For example, in a dataset of student grades, you might count how many students obtained grade A, how many obtained grade B and so on. These counts help summarize the distribution of data and are the basis for computing relative frequencies and percentages.

Step-by-Step Solution:
Step 1: Identify the variable of interest, such as gender, age group or response category. Step 2: List all distinct values or categories that occur for this variable. Step 3: For each category, count how many observations fall into that category. Step 4: Record these counts in a frequency table or chart. Step 5: Optionally, convert counts into relative frequencies or percentages by dividing each count by the total number of observations.

Verification / Alternative Check:
As an easy example, suppose you survey 10 people about their favorite fruit and get 4 responses for apple, 3 for banana and 3 for orange. The frequency of apple is 4, the frequency of banana is 3 and the frequency of orange is 3. These numbers are frequencies because they show how many cases fall into each category.

Why Other Options Are Wrong:
Option A describes calculating a product of variables, which is not what frequency means.
Option C misinterprets frequency as the number of times a dataset is used by a student, which is unrelated to the internal distribution of data values.
Option D describes calculating a sum over a column, which is an aggregate measure but not a frequency count of categories or values.

Common Pitfalls:
Learners sometimes confuse frequencies with measures like mean or sum. While mean and sum are numerical summaries, frequencies describe how often each category or value appears. Frequencies are particularly important in categorical data, where mean and standard deviation may not be meaningful.

Final Answer:
Calculating frequencies means counting the number of cases that fall into different subgroups within a dataset.