Mode Formula

Mode Formula

The article below discusses the Mode data, types of mode formula, its unit, and mode formula with solved examples.

Mode

Mode is a value that has a frequent database. When data frequently occurs in the database, we use the mode formula to find out the frequency of the data. The mode is classified into Unimode, bi-mode, tri-mode and multimodal lists based on the database.

• Unimodal: When a list of data has only one mode is known as a unimodal list.

• Bimodal: When a given data has two types of modes, it is called a Bimodal list.

• Multimodal: When data has various, or multiple modes are known as a multimodal list.

Mode Formula

Mode Formula is a value used to measure the given database called mode or modal value. In a shared database, the value which occurs at more frequency is called mode.

Mode Formula For Ungrouped Data

In a set of observations, when a particular value frequently occurs, the mode of the data can be determined by the highest frequency. 

Mode Formula For Grouped Data

When a data has distribution grouped frequency, the model can be calculated using the formula below.

 Mode = l + [(f₁ – f₀)/(2f₁ – f₀ – f₂)] × h

l = lower limit of the interval lower limit of the modal class

h = size of interval

f₁ = frequency 

f₀ = preceeding frequency  

f₂ = successive frequency 

Example 1

Calculate the mode for the given data 4, 9, 14, 27, 4, 4, 15, 9, 15, 27, 48, 37

Solution: 

The given data = 4, 4, 4, 9, 15, 15, 15, 27, 37, 48

A mode can be determined when a value occurs multiple times and has the highest frequency.

Hence, the numbers 4 and 15 have high frequency and consider the mode of the given database.

Example 2

A class has 30 students, and each student obtained various marks in mathematics. The below table represents the marks gained by the students out of 50 in mathematics. Find the mode for the given data.

Solution

The maximum frequency = 12

Class interval = 20-30

l = lower limit of the interval lower limit of the modal class = 20

h = size of interval – 10

f₁ = frequency = 12

f₀ = preceeding frequency = 5

f₂ = successive frequency = 8

Mode = l + [(f₁ – f₀)/(2f₁ – f₀ – f₂)] × h

Substitute the given value in the formula

 Mode = 20 + [(12 – 5)/(2 × 12 – 5- 8)] × 10

= 26.364