How to find Mode of Grouped and Ungrouped Data

Statistics refers to the collection, analysis, interpretation and presentation of masses of numerical data. In statistics, the most common measures of central tendency are the mean, median and mode. Each calculates the location of the central point using a different method.

The mode is the number that appears most frequently in a set of data. We can find the mode by counting the number of times each value occurs in a data set. In this article, we will discuss how to find the mode of grouped and ungrouped data.

What is Mode?

The observation with maximum frequency is called the mode. The equation for mode of grouped data is given by:

\(\begin{array}{l}Mode = l +\left ( \frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}} \right )\times h\end{array} \)

How to Calculate Mode Step by Step?

For grouped data:

Step 1. Find the maximum class frequency.

Step 2. Find the class corresponding to this frequency. It is called the modal class.

Step 3. Find the class size. (upper limit – lower limit.)

Step 4. Calculate mode using the formula.

\(\begin{array}{l}Mode =l +\left ( \frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}} \right )\times h\end{array} \)

Where l = the lower limit of modal class.

h = the size of class interval, (assuming classes are of equal size).

f₁ = the frequency of the modal class.

f₀ denotes the frequency of the class preceding the modal class.

f₂ denotes the frequency of the class succeeding the modal class.

For ungrouped data:

Find the observation which occurs the maximum number of times.

Formula

For grouped data,

\(\begin{array}{l}Mode = l +\left ( \frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}} \right )\times h\end{array} \)

Solved Examples

Example 1: A set of numbers consists of three 4s, five 5s, six 6s, eight 8s and seven 10s. The mode of this set of numbers is

(A) 6

(B) 7

(D) 10

Solution:

8 is represented 8 times. It comes maximum number of times. So, the mode is 8.

Hence option (c) is the answer.

Example 2:

Find the mode of the given data.

Class	Frequency
50-55	2
55-60	7
60-65	8
65-70	4

Solution:

Here 8 is the maximum class frequency

Here modal class is 60-65

Class size, h = 65-60 = 5

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

f₁ = 8

f₀ = 7

f₂ = 4

l = 60

So mode = 60 + ((8-7)/(16 – 7 – 4)]5

= 60 + (1/5)5

= 61

Mean, Median, Mode

Frequently Asked Questions

What is mode in statistics?

The observation with maximum frequency is called the mode.

Give the formula for finding the mode for grouped data?

For grouped data, mode = l + [(f₁ – f₀)h/(2f₁ – f₀ – f₂)].
Here l = the lower limit of modal class.
f₁ = the frequency of the modal class.
f₀ = the frequency of the class preceding the modal class.
f₂ = the frequency of the class succeeding the modal class.
h = the size of class interval, (assuming classes are of equal size).

How to find the mode for ungrouped data?

To find the mode for ungrouped data, find the observation that occurs the maximum number of times.

For any data set, which measures of central tendency have only one value?

For a given data set, the median and mean can only have one value. The mode can have more than one value.

How to Find Mode of Grouped and Ungrouped Data