Mode (Positional Average)

Mode is one of the three primary measures of central tendency, alongside Mean and Median. It refers to the most frequently occurring value in a data set. Unlike the mean and median, which are based on calculations and positioning, the mode emphasizes the frequency of values.

Understanding the mode is especially important in business contexts where identifying the most common value (like the most sold product size or popular price point) is useful for decision-making.

What is Mode?

Mode is the value that occurs most frequently in a dataset.
A dataset can have no mode, one mode (unimodal), two modes (bimodal), or multiple modes (multimodal).

Mode for Different Data Types

a. Individual Series

When raw data is listed without any frequencies.

Steps:

1. List the data values.

2. Identify the value(s) with the highest frequency.

Example:

Data: 12, 18, 14, 14, 16, 18, 14, 19

• 14 appears 3 times →

  $$\text{Mode}=14$$

b. Discrete Series

Data is provided along with frequency.

Steps:

1. Identify the variable $x$ with the highest frequency (f).

Example:

• Highest frequency = 8, corresponding to x = 30

  $$\text{Mode} = 30$$
  

c. Continuous Series (Grouped Data)

When data is in class intervals with frequencies.

Formula:

Where:

• $L$ = lower boundary of the modal class

• $f_1$ = frequency of the modal class

• $f_0$ = frequency of the class preceding modal class

• $f_2$= frequency of the class succeeding modal class

• $h$ = class width

Steps:

1. Identify the modal class (class with highest frequency).

2. Note the values for $f_1$, $f_0$, $f_2$, $L$, and $h$.

3. Apply the formula.

Example:

• Modal class = 20–30 (highest frequency = 12)

• $L=\mathrm{20, }$$f_1=\mathrm{12, }$$f_0=\mathrm{7, }$$f_2=\mathrm{9, }$$h=10$

Merits of Mode

• Easiest measure to identify in many cases.

• Useful for categorical data (e.g., most sold brand).

• Not affected by extreme values.

• Represents the most typical case.

Demerits of Mode

• May not be unique (bimodal/multimodal).

• Not based on all data values.

• Less useful in small datasets with no repetition.

• Difficult to compute accurately for grouped data without interpolation.

Mean vs. Median vs. Mode

Conclusion

Mode is an important and practical measure of central tendency, especially useful for identifying the most common value in a dataset. While it has limitations in terms of calculation and uniqueness, its value lies in analyzing consumer preferences, market trends, and categorical data.