Construction of Frequency Distribution

The number of classes typically ranges between 5 and 20, depending on your data density. Fewer classes work well for smaller datasets, while larger datasets benefit from more classes to capture variation. The choice affects how detailed your frequency distribution becomes and how clearly patterns emerge in your data.

Class width represents the range of values within each class. Calculate it by subtracting the smallest value from the largest value to find the range, then divide that range by the number of classes. Round the result up for convenience to ensure all data points fit within your classes.

The minimum value in your dataset becomes the first lower-class limit. Add the class width to this value to find the second lower-class limit, then repeat for remaining classes. For upper-class limits, subtract one from the second lower-class limit to get the first upper-class limit, then calculate the rest similarly.

Tally marks track how many data points fall within each class interval. Place one mark for each observation in the appropriate class, then sum all marks in a class to determine its frequency. This counting method ensures accurate frequency calculations and prevents data entry errors.

Use a grouped frequency distribution when your dataset contains large sets of different values. Grouping organizes data into classes, making patterns easier to identify and the table more readable. An ungrouped distribution works better for smaller datasets with fewer distinct values.

Create a table with columns for data values and frequency. Decide whether grouped or ungrouped organization suits your data. List values in the first column, count how often each appears, and record frequencies in the second column. Finally, calculate the total frequency by summing all individual frequencies.

A frequency distribution summarizes how data varies across categories or ranges, revealing patterns that raw data obscures. For marathon participants, it shows how many runners fall into each age group, making it easy to see which ages are most represented. This organized format supports further analysis and visualization through methods like a relative frequency distribution.