Modal Class
Modal class or the mode class is the class interval in a frequency distribution table that contains the highest frequency. While calculating the mode in statistics, modal class plays a significant role especially while calculating the mode of grouped data. Let us learn more about the modal class, the formula, and solve a few examples.
1.  Definition of Modal Class 
2.  Modal Class Formula 
3.  How to Find the Modal Class? 
4.  FAQs on Modal Class 
Definition of Modal Class
In statistics, the class interval with the highest frequency is defined as a modal class. The frequency in the class interval is the highest in a continuous quantitative distribution where the values are grouped into classes with similar dimensions. Mode is not used as a measure of central tendency for continuous quantitative variables since it is more helpful for qualitative variables. Hence, to calculate the mode of grouped data, the middle range of the modal class is used. In other words, mode can't be obtained just by looking into the frequency, we first need to find out the modal class, in which lies the mode of the given data.
Example: Determine the modal class from the given frequency table
Balls  10090  9080  8070  7060  6050  5040  4030 
Boxes  96  32  54  12  27  69  81 
Solution:
As we already know that mode is the number that appears the most. To find the modal class, we first arrange the frequencies in ascending order to look for the class with the highest frequency. The class with the highest frequency will be considered as the modal class that also contains the mode. Since the modal class is the class in grouped data that contains the mode. The given frequencies are:
96, 32, 54, 12, 27, 69, 81
Let us arrange them in ascending order to find the highest frequency.
12, 27, 32, 54, 69, 81, 96
The highest frequency from the above list is 96 and the class interval corresponding to it is 10090.
Therefore, the modal class is 10090.
Modal Class Formula
To calculate the modal class, the formula for mode of grouped data is used. Let us understand the different terms used in the formula that helps us derive the value of the modal class. For any given data range, let us consider L is the lower limit of the modal class, h is the size of the class interval, f_{m} is the frequency of the modal class, f_{1} is the frequency of the class preceding the modal class, and f_{2} is the frequency of the class succeeding the modal class. Here, the modal class is the data interval with the highest frequency. Thus, the mode can be calculated by the formula:
Mode = \(L+h \frac{\left(f_{m}f_{1}\right)}{\left(f_{m}f_{1}\right)+\left(f_{m}f_{2}\right)}\)
where,
 L is the lower limit of the modal class
 h is the size of the class interval
 \(\mathrm{f}_{\mathrm{m}}\) is the frequency of the modal class
 \(\mathrm{f}_{\mathrm{1}}\) is the frequency of the class preceding the modal class
 \(\mathrm{f}_{\mathrm{2}}\) is the frequency of the class succeeding the modal class
We might find the above formula written in different forms in some references, as given below,
Mode = \(I_{0}\) + \(\left(\frac{f_{1}f_{0}}{2 f_{1}f_{0}f_{2}}\right) h\)
Here,
 I\(_0\) is the lower limit of the modal class
 h is the size of the class interval
 \(\mathrm{f}_{\mathrm{1}}\) is the frequency of the modal class
 \(\mathrm{f}_{\mathrm{0}}\) is the frequency of the class preceding the modal class
 \(\mathrm{f}_{\mathrm{2}}\) is the frequency of the class succeeding the modal class
How to Find Modal Class?
Let us look at an example of finding the modal class along with the mean using the modal class formula.
Class Interval  0−5  5−10  10−15  15−20  20−25 

Frequency  5  3  7  2  6 
Modal class = 10  15 (This is the class with the highest frequency). The Lower limit of the modal class = (L) = 10, Frequency of the modal class = \((f)_{m}\) = 7, Frequency of the preceding modal class = \((f)_{1}\) = 3, Frequency of the next modal class = \((f)_{2}\) = 2, and Size of the class interval = (h) = 5. Thus, the mode can be found by substituting the above values in the formula: Mode = L + h \(\begin{align}\dfrac{(f_mf_1)}{(f_mf_1)+(f_mf_2)}\end{align}\) .
Thus, Mode = 10 + 5 \(\begin{align}\dfrac{(73)}{(73)+(72)}\end{align}\) = 10 + 5 × 4/9 = 10 + 20/9 = 10 + 2.22 = 12.22.
Therefore the mode for the above dataset is 12.22.
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Important Notes on Modal Class
 In a frequency distribution, the class that consists of the highest frequency is known as the modal class.
 The modal class is the class that will consist of the mode.
 The formula to find the modal class is given as \(I_{0}\) + \(\left(\frac{f_{1}f_{0}}{2 f_{1}f_{0}f_{2}}\right) h\).
Examples on Modal Class

Example 1: Josie has the weight of 100 employees from her organization. She needs to find the modal class from the given table. What would the modal class be?
Weights 6070 7075 7595 95100 Frequency 43 26 24 7 Solution:
Given the frequencies,
43, 26, 24, 7
Let us arrange this in ascending order,
7, 24, 26, 43
The class interval with the highest frequency is considered the modal class.
Looking at the frequencies, the highest is 43.
Therefore, the modal class is 6070.

Example 2: Find the mode for the grouped data and the modal class for the class interval and frequency mentioned in the table.
The age group of employees 20  30 30  40 40  50 50  60 Number of people of that age 40 55 34 20 Solution:
Modal class = 30  40 (This is the class with the highest frequency). Lower limit of the modal class = (L) = 30, Frequency of the modal class = \((f)_{m}\) = 55, Frequency of the preceding modal class = \((f)_{1}\) = 40, Frequency of the next modal class = \((f)_{2}\) = 34, and Size of the class interval = (h) = 10. Thus, the mode can be found as:
Mode = L + h \( \dfrac{(f_mf_1)}{(f_mf_1)+(f_mf_2)} \)
Thus, Mode = 30 + 10 \( \times \frac{(5540)}{(5540) + (5534)} \) = 30 + 10{15/(15 + 21)} = 30 + 150/36 = 30 + 4.67 = 34.67.
Therefore, the modal class is 30  40 and the mode is 34.67.
FAQs on Modal Class
What is Modal Class?
Modal class is the class interval that has the highest frequency in the continuous quantitative distribution. The modal class is usually used while finding the mode of grouped data.
What is Modal Class in Mode?
Mode is the number that appears more often and modal class is the class interval with the highest frequency. Hence, the modal class is the class in grouped data that contains the mode.
What If There are 2 Modal Classes?
There can be cases when a number repeats twice on a frequency table that means there are two modes and it is called bimodal. If there are more than 3, it is called multimodal. And these class intervals will be considered as the modal class. If there are numbers that appear the same number of times, then there is no mode.
Can You Have Two Modal Classes?
If there are 2 modes in a frequency table, it is called bimodal. The modal class will be according to the modes since the modal class contains the modes. The twoclass intervals will be preceding each other.
How Can You Find the Modal Class?
The modal class is the class interval with the highest frequency in a frequency table. To find the modal class, we need to arrange the frequencies in an ascending order to find the highest frequency. Once the number is found, the class interval corresponding to the number is the modal class.
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