Mode of Grouped Data

In statistics, we have learned that the mode is the most repeated value among the given set of data. Among the given set of observations, mode is the value which has the maximum frequency. Sometimes, it is possible to have more than one value which has the same maximum frequency. In such a case, we can say that the data is multimodal. In this article, we are going to learn how to find the mode of ungrouped and the grouped data with its formula and solved examples.

Table of Contents:

• Finding Mode of Ungrouped Data
• How to Find the Mode of Grouped Data
• Example
• Practice Problems
• FAQs

Finding Mode of Ungrouped Data

Before learning about how to find the mode of grouped data, we will have a look at how to find the mode of ungrouped data.

For example, the wickets taken by a bowler in 10 cricket matches are 2, 6, 4, 5, 0, 2, 1, 3, 2, 3. Find the mode of the given data.

To find the mode of the ungrouped data, first construct the frequency distribution table.

So, it is clearly observed that, 2 is the number of wickets taken by the bowler in the maximum number of cricket matches i.e., 3. Therefore, the mode of the given data is 2.

Hence, we can easily determine the mode of the given data, if it is ungrouped.

How to Find the Mode of Grouped Data?

In the case of grouped data, it is not possible to identify the mode of the data, by looking at the frequency of data. In this scenario, we can determine the mode value by locating the class with the maximum frequency called modal class. Inside a modal class, we can locate the mode value of the data by using the formula,

Where,

f₁ is the frequency of the modal class

f₀ is the frequency of the class preceding the modal class

f₂ is the frequency of the class succeeding the modal class

h is the size of the class intervals

l is the lower limit of the modal class

Now, let us understand how to find the mode of grouped data using this formula with the help of an example.

Mode of Grouped Data Example

Question:

A survey has been conducted by a group of students on 20 households in a locality as shown in the following frequency distribution table. Find the mode for the given data.

Solution:

From the given table, it is observed that the maximum class frequency is 8, and the corresponding class interval is 3-5.

Therefore, the modal class for the given data is 3-5.

The lower limit of modal class, l = 3

Class size, h = 2

Frequency of modal class, f₁ = 8

Frequency of class proceeding to modal class, f₀ = 7

Frequency of class succeeding to modal class, f₂ = 2

We know that the formula to find the mode of the grouped data is:

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

Mode = 3 + (2/7)

Mode = (21+2)/7

Mode = 23/7

Mode = 3.286.

Therefore, the mode of the given grouped data is 3.286.

Practice Problems

1. The information on the observed lifetimes (in hours) of 225 electrical components are given in the following frequency table. Find the modal lifetimes of the electrical components.

   The lifetime of electrical components (in hours)	0-20	20-40	40-60	60-80	80-100	100-200
   Frequency	10	35	52	61	38	29

2. The following distribution table shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Find the mode of the given data.

   Runs scored by Top Batsmen	Number of Batsmen
   3000 – 4000	4
   4000 – 5000	18
   5000 – 6000	9
   6000 – 7000	7
   7000 – 8000	6
   8000 – 9000	3
   9000 – 10000	1
   10000- 11000	1

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