Understanding Relative and Cumulative Relative Frequency

The Relative Frequency of a value in a dataset is the proportion of times that value occurs compared to the total number of data points. It shows how often a particular value appears relative to the total number of observations.

Formula for Relative Frequency

The Cumulative Relative Frequency is the accumulation of the relative frequencies. It is the running total of relative frequencies, showing the proportion of values that are less than or equal to a certain value in the dataset.

Example Calculation

Let's calculate the relative and cumulative relative frequencies for the following dataset:

• Data: [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]

Step-by-step:

1. Find the frequency of each value:
• 1 appears 1 time
• 2 appears 2 times
• 3 appears 3 times
• 4 appears 4 times
2. Calculate the relative frequency for each value:
• \( \text{Relative Frequency of 1} = \frac{1}{10} = 0.10 \)
• \( \text{Relative Frequency of 2} = \frac{2}{10} = 0.20 \)
• \( \text{Relative Frequency of 3} = \frac{3}{10} = 0.30 \)
• \( \text{Relative Frequency of 4} = \frac{4}{10} = 0.40 \)
3. Calculate the cumulative relative frequency:
• Cumulative relative frequency for 1 = 0.10
• Cumulative relative frequency for 2 = \( 0.10 + 0.20 = 0.30 \)
• Cumulative relative frequency for 3 = \( 0.30 + 0.30 = 0.60 \)
• Cumulative relative frequency for 4 = \( 0.60 + 0.40 = 1.00 \)

Therefore, the relative and cumulative relative frequencies for this dataset are calculated as shown.

Further Reading

• Frequency in Statistics on Wikipedia
• Explore More Calculators on Research Data Pod