How do you find the relative frequency of a mode?

To find the relative frequency of a mode, you first identify the mode, which is the most frequently occurring value in a dataset. Then, you calculate its relative frequency using the formula: (Frequency of the Mode / Total Number of Data Points).

Understanding the Terms

Let's break down the key terms:

• Mode: The value that appears most often in a dataset. A dataset may have one mode (unimodal), two modes (bimodal), or more (multimodal). If no value repeats, there's no mode.
• Frequency: The number of times a specific value appears in the dataset.
• Relative Frequency: The proportion of times a specific value appears relative to the total number of values in the dataset. It's usually expressed as a fraction, decimal, or percentage.

Calculating Relative Frequency of the Mode

Here’s a step-by-step guide:

1. Identify the Mode: Determine the most frequent value(s) in your dataset.
   • Example: In the dataset [2, 3, 3, 4, 5, 3, 6], the mode is 3 because it appears three times, which is more than any other number.
2. Find the Frequency of the Mode: Count how many times the mode appears.
   • Example: In the same dataset, the frequency of the mode (3) is 3.
3. Determine the Total Number of Data Points: Count all the individual values in the dataset.
   • Example: The total number of data points in the example dataset is 7.
4. Divide the Frequency of the Mode by the Total Number of Data Points: This gives you the relative frequency.
   • Formula: Relative Frequency of Mode = (Frequency of the Mode) / (Total Number of Data Points)
   • Example: The relative frequency of the mode (3) is 3 / 7, which is approximately 0.4286 or 42.86%

Example

Let’s illustrate with another example:

Consider the dataset: [10, 12, 15, 12, 18, 12, 20, 22]

• Mode: 12 (appears 3 times).
• Frequency of Mode: 3
• Total Data Points: 8
• Relative Frequency of the Mode: 3 / 8 = 0.375 or 37.5%.

Practical Insights and Applications

• Understanding Data Distribution: Relative frequency helps understand the distribution of data. It shows how often the mode appears compared to other values.
• Comparative Analysis: You can compare relative frequencies of modes across different datasets to see which has a more prominent mode.
• Data Interpretation: Relative frequency provides a more meaningful understanding than just frequency, especially when dealing with datasets of varying sizes.

Summary Table

Step	Description	Example
1. Identify the Mode	Find the most frequently occurring value.	In [2,3,3,4,5,3,6], the mode is 3
2. Frequency of the Mode	Count how many times the mode appears.	The frequency of 3 is 3
3. Total Data Points	Count all values in the data set.	There are 7 total data points
4. Calculate Relative Frequency	Divide the frequency of mode by the total data points	3 / 7 ≈ 0.4286 or 42.86%

Reference

• "For each category, divide the frequency by the total number of data points to get the relative frequency. This is often expressed as a percentage or a fraction." [Source Date: 28-Apr-2022]