Relative frequency and cumulative frequency are two important concepts in statistics that are used to analyze and interpret data.
Relative Frequency: This refers to the ratio of the number of times a particular event occurs to the total number of events observed. It is often expressed as a decimal or a percentage. For example, if we have a survey of 100 people and 30 of them prefer coffee over tea, the relative frequency of coffee preference is 30/100 = 0.3 or 30%. Relative frequency provides insights into how common or popular an option is within a given dataset.
Cumulative Frequency: On the other hand, cumulative frequency is the running total of frequencies up to a certain point in the data. It is calculated by adding the frequency of a particular class to the cumulative frequency of the previous classes. For instance, if we have classes of scores (0-10, 11-20, etc.) and their respective frequencies, the cumulative frequency for the score range of 11-20 would include the frequency of both the 0-10 range and the 11-20 range combined. This is useful for understanding how many observations fall below a particular value and helps in determining percentiles or quartiles.
Key Difference: In summary, relative frequency gives us a sense of how often an event occurs in relation to the total, while cumulative frequency helps us understand the total occurrences up to a certain point. Both metrics serve different purposes in data analysis, with relative frequency focusing on the distribution of data and cumulative frequency on the accumulation of data points.