Learn Mode of Grouped Data with Solved Examples - Testbook

In statistics, the mode is the value that occurs most often in a data set. It tells us which value is the most common or frequently repeated. A data set can have one mode (called unimodal), more than one mode (bimodal or multimodal), or no mode at all if all values occur the same number of times. The mode is one of the three main measures of central tendency, along with the mean and median. It helps us understand the pattern or trend in a set of numbers. This topic is especially useful when dealing with large sets of data, such as survey results or marks scored by students. In this article, you’ll learn how to find the mode for ungrouped data (individual values) and grouped data (data divided into class intervals). We'll explain the formulas and give simple examples to help you understand the concept clearly.

Contents:

• Calculating Mode of Ungrouped Data
• Calculating Mode of Grouped Data
• Example
• Practice Problems

Calculating Mode of Ungrouped Data

Before diving into the calculation of the mode for grouped data, let's first understand how to calculate the mode for ungrouped data.

For instance, consider the number of goals scored by a football player in 10 matches are 1, 3, 2, 4, 3, 2, 2, 3, 4, 2. How do we find the mode of this data set?

To find the mode of ungrouped data, we begin by constructing a frequency distribution table .

Number of Goals	1	2	3	4
Number of Matches	1	4	3	2

From the table, it is evident that the number 2 is scored most frequently in the matches, i.e., 4 times. Therefore, the mode of the given data is 2.

Calculating Mode of Grouped Data

For grouped data, the mode isn't as straightforward to identify as it is for ungrouped data. In this case, we find the mode by identifying the class with the highest frequency, known as the modal class. We then calculate the mode within the modal class using the formula:

Where,

f 1 is the frequency of the modal class

f 0 is the frequency of the class before the modal class

f 2 is the frequency of the class after the modal class

h is the class width

l is the lower class boundary of the modal class

Now, let's illustrate the calculation of the mode for grouped data using this formula with a different example.

Grouped Data Mode Example

Example:

A research team conducted a survey on the number of pets in 20 households in a neighborhood. The results are represented in the frequency distribution table below. Calculate the mode for the given data.

Number of Pets in Household	1-2	2-3	3-4	4-5	5-6
Number of Households	5	9	3	2	1

Solution:

The table shows that the highest frequency is 9, corresponding to the 2-3 class interval.

Therefore, the modal class for the given data is 2-3.

The lower limit of modal class, l = 2

Class width, h = 1

Frequency of modal class, f 1 = 9

Frequency of class before modal class, f 0 = 5

Frequency of class after modal class, f 2 = 3

Applying these values to the mode formula , we find:

Mode = 2 + (4/10)

Mode = 2.4

Therefore, the mode of the given grouped data is 2.4.

1. The table below represents the lifespan (in hours) of 225 light bulbs. Find the modal lifespan.

Lifespan of Light Bulbs (in hours)	0-1000	1000-2000	2000-3000	3000-4000	4000-5000	5000-6000
Frequency	20	45	60	50	30	20

1. 
   The distribution table below shows the number of runs scored by some of the world's top cricketers in one-day international matches. Calculate the mode of the given data.

Runs Scored by Top Cricketers	Number of Cricketers
2000 – 3000	5
3000 – 4000	15
4000 – 5000	10
5000 – 6000	7
6000 – 7000	6
7000 – 8000	4
8000 – 9000	2
9000 – 10000	1

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