Data Presentaion
Grouped and Ungrouped Frequency Distribution Tables In statistics, a frequency distribution table is used to organize data and show how often each value or range of values occurs. There are two types of frequency distribution tables:
Ungrouped Frequency Distribution Table
An ungrouped frequency distribution presents individual data values along with their corresponding frequencies. This is used when data is small and values are distinct. The specific values matter and don’t need categorization.
Let's consider a class survey where students are asked how many books they read in a month. The collected responses are:
Data Set: 2, 3, 3, 2, 4, 2, 5, 3, 3, 4, 2, 5, 4, 3, 2
| Number of Books (x) | Frequency (f) | Tally Marks |
|---|---|---|
| 2 | ||
| 3 | ||
| 4 | ||
| 5 |
Grouped Frequency Distribution Table
A grouped frequency distribution classifies data into intervals (classes) and shows the frequency of data points within each class. When the dataset is large and has a wide range of values. To make data easier to analyze and visualize.
Suppose we record the marks (out of 50) of 30 students in a test:
Raw Data: 5, 9, 12, 14, 17, 19, 21, 22, 25, 27, 29, 31, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 49
We can group this data into class intervals of size
| Marks Range (Class Interval) | Frequency (f) | Tally Marks |
|---|---|---|
| 0 - 10 | ||
| 11 - 20 | ||
| 21 - 30 | ||
| 31 - 40 | ||
| 41 - 50 |
This method groups the data into intervals (e.g., 0–10, 11–20) instead of listing individual values.
Key Differences Between Grouped and Ungrouped Frequency Tables
| Feature | Ungrouped Frequency Table | Grouped Frequency Table |
|---|---|---|
| Data Representation | Lists individual values | Uses class intervals (ranges) |
| Used for | Small datasets | Large datasets |
| Ease of Interpretation | Simple for small data but difficult for large data | Easier for large datasets |
| Example | Number of siblings in a class | Heights of students in a school |