1. Ungrouped Data
Ungrouped data is data that is listed as individual values, without putting them into any intervals or categories. It shows every value exactly as it was collected.
This form is useful when the number of observations is small or when each value needs to be seen separately.
1.1. Example of Ungrouped Data
Suppose the number of chocolates eaten by a group on different days is:
3, 5, 2, 5, 1, 3, 4
Each value is shown individually. No grouping is done.
2. Grouped Data
Grouped data is formed by arranging values into intervals called class intervals. This helps when the data range is large or when there are many observations. Grouping makes it easier to identify patterns and understand how the values are spread.
2.1. Class Intervals
Class intervals are ranges like 0–10, 10–20, 20–30, and so on. Each interval collects values that fall within that range.
2.2. Example of Grouped Data
For the data: 12, 18, 25, 29, 34, 36, 40, 42, 45 — grouping into intervals gives:
| Interval | Frequency |
|---|---|
| 10–20 | 2 |
| 20–30 | 2 |
| 30–40 | 2 |
| 40–50 | 3 |
3. Difference Between Grouped and Ungrouped Data
The difference comes from how the data is shown—either individually or in intervals.
3.1. Quick Comparison
- Ungrouped data shows every value separately.
- Grouped data arranges values into class intervals for easier analysis.
- Ungrouped data is clear when the number of values is small.
- Grouped data is better when handling large or spread-out values.