1. Meaning of Frequency
Frequency tells how many times a particular value or item appears in the data. Instead of writing every value again and again, frequency helps count repeated values easily.
For example, if the marks 5 appears 3 times in a list, then the frequency of 5 is 3.
2. Frequency Table for Ungrouped Data
Ungrouped data lists each value separately. A frequency table for such data helps count how often each value appears. It is useful when the number of distinct values is small.
2.1. Steps to Create an Ungrouped Frequency Table
- Write all the different values in one column.
- Go through the data list and count how many times each value appears.
- Write the counts in another column as frequencies.
2.2. Example
Consider the data: 2, 3, 2, 5, 3, 3, 4, 2.
| Value | Frequency |
|---|---|
| 2 | 3 |
| 3 | 3 |
| 4 | 1 |
| 5 | 1 |
3. Frequency Table for Grouped Data
When the data has many values or varies over a wide range, grouping it into intervals (called class intervals) makes it easier to analyze. Each interval shows how many data points fall within that range.
3.1. Class Intervals
Class intervals group values into ranges such as 0–10, 10–20, 20–30, and so on. The width of each interval is the difference between its upper and lower limits.
3.2. Steps to Create a Grouped Frequency Table
- Choose suitable class intervals based on the data range.
- Make sure intervals cover all values without gaps.
- Count how many values fall in each interval.
- Record the counts as frequencies.
3.3. Example
For the data: 12, 18, 25, 29, 34, 36, 40, 42, 45, we group into intervals:
| Class Interval | Frequency |
|---|---|
| 10–20 | 2 |
| 20–30 | 2 |
| 30–40 | 2 |
| 40–50 | 3 |