To find the relative frequency in statistics, divide the frequency (number of occurrences) of a specific value by the total number of values in the dataset. This provides the proportion of times that value occurs.
Here's a more detailed breakdown:
1. Understand Frequency:
- Frequency refers to the number of times a particular value appears in a dataset. For example, if you surveyed 20 people about their favorite color and 5 said "blue," the frequency of "blue" is 5.
2. Calculate Relative Frequency:
-
Relative Frequency = (Frequency of the Value) / (Total Number of Values)
In the color example:
- Frequency of "blue" = 5
- Total number of values (total people surveyed) = 20
- Relative frequency of "blue" = 5 / 20 = 0.25
3. Expressing Relative Frequency:
- Relative frequency can be expressed as a decimal (like 0.25), a fraction (like 1/4), or a percentage (like 25%). To convert a decimal to a percentage, multiply by 100.
Example:
Let's say you have the following set of data representing the ages of 10 people: 10, 12, 10, 14, 12, 10, 16, 12, 10, 12
| Age | Frequency | Relative Frequency |
|---|---|---|
| 10 | 4 | 4/10 = 0.4 (or 40%) |
| 12 | 4 | 4/10 = 0.4 (or 40%) |
| 14 | 1 | 1/10 = 0.1 (or 10%) |
| 16 | 1 | 1/10 = 0.1 (or 10%) |
| Total | 10 | 1 |
4. Cumulative Relative Frequency (Optional):
- Cumulative relative frequency represents the accumulated relative frequency up to a certain point in the data. To calculate it, add the relative frequency of the current value to the cumulative relative frequencies of all previous values. This is usually used when the data is ordered in some meaningful way (e.g., age ranges, income brackets).
Example (using the age data, and ordering ages ascending):
| Age | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 10 | 4 | 0.4 | 0.4 |
| 12 | 4 | 0.4 | 0.4 + 0.4 = 0.8 |
| 14 | 1 | 0.1 | 0.8 + 0.1 = 0.9 |
| 16 | 1 | 0.1 | 0.9 + 0.1 = 1.0 |
In Summary:
Relative frequency is a fundamental concept in statistics that helps you understand the distribution of data by showing the proportion of times each value occurs within the dataset. It's calculated by dividing the frequency of a specific value by the total number of values.
