How to Use Mode Formula in Statistics: Your Step-By-Step Guide

Have you ever wondered which flavour of ice cream is the most popular? Or maybe you're curious about the most common shoe size? The answer to these questions lies in understanding the mode! This article dives into the world of mode, a key concept in statistics. We'll explore what the mode is, why it's important, and, most importantly, how to find the mode using a simple formula. So, whether you're a data whiz or just starting your statistical journey, this guide will equip you to identify the most frequent value in any dataset.

Like the mean and median, the mode is also a measure of central tendency representing the most frequently occurring value in the dataset. While it is less useful in comparison to the mean and median, but when it comes to categorical data (nominal and ordinal data), the mode is the best measure of central tendency.

This article will discuss the mode formula, how to find the mode of grouped and groped data, the advantages and disadvantages of the mode formula, and at the end, some examples to better understand mode.

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So, let’s dive deep to know more about the statistical mode formula.

Table of Content

• What is Mode in Statistics?
  • Examples: When to use Mode
• How to Calculate the Mode?
  • Mode Formula for Ungrouped Data
  • Mode Formula for Grouped Data
• Advantages and Limitations

What is Mode in Statistics?

In statistics, the mode (or modal) is the measure of central tendency that represents the most frequent data in the dataset. In simple terms, the value that appears the maximum number (highest frequency) of times in the dataset is known as a mode. It is very useful while dealing with the nominal dataset.

Example: 

Suppose a political strategic company wants to analyze the most preferred candidate for the upcoming elections. The results of the survey for a group of 15 people are as follows: A, A, B, A, C, D, A, A, A, B, B, B, C, A, A. In the above survey, the candidate ‘A’ appears most frequently. 

The political company can use this data to suggest the political party to choose the best candidate (most preferred) for the elections.

Scenarios where Mode is the best Measure of Central Tendency

1. Nominal Data: Mode is the only measure of central tendency that is used for nominal data (categorical data without any numerical significance).

2. Skewed Data: In the case of skewness, the mode is a better measure than the mean and median as it identifies the most frequently occurring value.

3. Binomial Data: The set is called binomial data if two values occur equally in the dataset. In this case, the mode is the best measure of central tendency, as it measures the most frequently occurring values.

4. Sparse Data: When the dataset contains many values that occur once, twice, or thrice, the mode can be the best measure. Since the mean can be affected by these outliers, and the median may not be the best representative.

Now, it’s time to know how to calculate the mode: Formula and Steps.

How to Calculate the Mode?

This section will contain the mode formulas for ungrouped and grouped data, steps to find mode, examples, and some real-world applications of mode.

Mode Formula for Ungrouped Data

To calculate the mode of the ungrouped data, you have to follow these simple steps:

• Arrange the dataset in order (either ascending or descending)
• Count the frequency of each data value.
• Identify the value that appears most frequently.

Now let’s take an example to find the mode of the ungrouped data.

Example: Suppose you have the following sets of numbers: 5, 7, 8, 2, 5, 9, 5, 8, 6, 7, 5, 3, 2, 4, 5, 9, 1.

Solution: 

Firstly, arrange the dataset in order (here ascending order): 1, 2, 2, 3, 4, 5, 5, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9

Let’s arrange the count of the frequency in a tabular form.

Numbers	1	2	3	4	5	6	7	8	9
Frequency	1	2	1	1	5	1	2	2	2

Here, from the above table, the value that appears most frequently is 5.

Hence, the mode is 5.

Mode Formula for the Grouped Data

To calculate the mode of the grouped data, follow these simple steps:

• Identify the class interval in the frequency distribution with the highest frequency.
  • This is the modal class interval.
• Now, use the below formula to calculate the mode.

Mode = L + ((f1 – f0) / (2f1 – f0 – f2)) x h,

where

L: Lower limit of the modal class

f0: frequency of the class before the modal class (preceding the modal class)

f1: frequency of the modal class

f2: frequency of the class after the modal class (succeeding the modal class)

h: the size of the class interval

Now let’s take an example to find the mode of the grouped data.

Example: Consider the following grouped data

Class Interval	Frequency
0-10	5
10-20	15
20-30	20
30-40	25
40-50	20
50-60	10

Solution

From the above, firstly identify the modal class, i.e., the class with the highest frequency

Here, the highest frequency is 25; therefore the modal class will be 30-40.

So,

L = 30

f0 = 20

f1 = 25

f2 = 20

h = 10

Now, substituting the above values in the mode formula, we get:

Mode = 30  + ((25-20) / (2*25 – 20 – 20)) * 10 = 30 + (5 / 10) * 10

=> Mode = 30 + 5

=>  Mode = 35

Hence, the mode of the above-grouped data is 35.

Advantages and Disadvantages of Mode

Advantages of Mode

• Easy to calculate and reflects the most common value in the data set.
• Not influenced by the extreme values or the outliers in the dataset.
• Only the measure of central tendency is applicable to the nominal data.
• In the case of nominal, skewed, Binomial and sparse data, the mode is better than the mean and median.

Limitations of Mode

• Mode is not applicable over continuous data.
• Mode only provides the information corresponding to the most frequent value in the data set; it doesn’t provide any information about the data's spread or variability.
• Mode may or may not be unique.
  • It is also possible that for any given dataset mode doesn’t exist.
• Mode is highly unstable, i.e., a very small change in the dataset may change the mode.

Conclusion

In conclusion, the mode statistics formula is the measure of central tendency that represents the most frequently occurring observations from the given number of observations. This article briefly discusses the mode in statistics, cases where mode outperforms mean and median, and how to calculate the mode for grouped and ungrouped data. And later, it also discussed the advantages and limitations of the mode.

Hope you will like the article.

Happy Learning!!

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