Mode Formula: Find Mode for Grouped and Ungrouped Data

Mode Formula: Mode is one of the values that indicate a central tendency of a set of data. Mode or modal value gives us an idea about which of the items in a data set is more likely to occur frequently. It is the measure of Central Tendency other than Mean and Median. The mode can easily be found for a finite set of data or observations. We can find the mode of data with normal data set, group data set and non-grouped or ungrouped data set. However, the formula to find the mode in the two sets of data is different.

Depending on the type of dataset given, you can find one, two three or even multiple modal values. Some data sets may have no mode value at all. In this article, we will talk about the mean median mode formula class 10 in detail.

What Is Mode Formula?

The formula that is used for the purpose of finding the mode of grouped or non-grouped data is called the formula for mode and the value of the observation with the maximum frequency is called mode. The formula for calculating mode is mentioned below:

Mode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

Where,

l = lower limit of the modal class
h = size of the class interval
f₁ = frequency of the modal class
f₀ = frequency of the class preceding the modal class
f₂ = frequency of the class succeeding the modal class

Let us help you understand and use the above mode formula Class 10 in statistics effectively through an example. Before going into the mathematical formula for finding mode, let us take a look at an example to understand what mode is.

The runs scored by a batsman in 10 cricket matches are as follows:

Mode is given as the value among the observation that occurs most often. So, the mode of this data is 10. In the below sections, we have mentioned the mode formula with examples for better understanding.

Mode Formula With Examples

If the data is ungrouped, it is very easy to find the mode as it is the value that appears most often. An example of such type is:

Mode Of Ungrouped Data

Sample Problem 1: Find the mode of the given data set: 4, 4, 6, 10, 18, 18, 18, 30, 30, 40, 51.

Solution: In the following list of numbers 4, 4, 6, 10, 18, 18, 18, 30, 30, 40, 51. and 18 appears the maximum number of time and therefore it is the mode.

Sample Problem 2: Find the mode of 5, 5, 5, 10, 16, 16, 16, 28, 38, 49 data set.

Solution: In the given data set both 5 and 16 appear the max number of times i.e. 3 therefore, the mode is both 5 and 16.

Fact Update: Any given data set or values can have more than one mode if more than one value occurs with equal frequency and number of times compared to the other values in the set.

Sample Problem 3: Find the mode of 2, 5, 8, 15, 26, 36, 47.

Solution: There can be data set that do not have a mode and one such example is the above question

So, for data set 2, 5, 8, 15, 26, 36, 47 there is no mode available.

Mode Of Grouped Data

Now we will take the example of grouped data and how to use the above-explained formula to calculate the mode.

Example 1: A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

Find the mode for the above data.

Solution 1: Here the maximum class frequency is 8, and the class corresponding to this frequency is 3 – 5. So, the modal class is 3 – 5.

Now

– Modal class = 3 – 5, lower limit (l) of modal class = 3, class size (h) = 2
– Frequency (f₁) of the modal class = 8, frequency
– (f₀) of class preceding the modal class = 7,
– Frequency (f₂) of class succeeding the modal class = 2.

Putting the values in the formula:

Mode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\)

Mode = 3 +\(\frac{8-7}{2×8-7-2}\times 2\) = 3.286.

Mean Median Mode Formula

In your home exams, you will be asked to calculate all 3 i.e mean, median, and mode for a given data set:

Let us consider the following data set 3, 3, 5, 6, 8.

Now you know the basic mode calculation formula to calculate the mode of a dataset. However, it is important to understand the concepts behind mode thoroughly and do more practice to master this important topic. Embibe offers interactive and fun videos that will help students to learn difficult concepts easily. Watch these videos to understand mode and several other mathematics topics in depth.

FAQs on Mode Formula in Statistics

Here are some relevant questions on the topic:

Q. How do you find the mode in a frequency table?
Ans: In a frequency table, you must find the values of the various elements of the mode formula and then put the values in the formula to calculate the mode.

Q. What is the formula for mode and median?
Ans: The formula to calculate mode and median is provided below:
Median:
[(n/2)^th term + {(n/2)+1}^th term]/2 (when n is even)
{(n+1)/2}^th term (when n is odd)
Mode = l +\(\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h\).

Q. How do you use the simple Mode formula?
Ans: How to effectively use the formula has been explained with an example on this page. The formula is only valid for grouped data as for ungrouped data you can find the mode by directly looking at the data set.

Q. What is a mode?
Ans: A mode is a number in a set of data that repeats itself the maximum number of times. For instance, in the set: 1, 2, 3, 4, 2, 2, 9, 7, 8, 6, 5, 4, the mode is 4.

Q. Is it possible to not have any Mode for a set of data?
Ans: Yes, this is possible. In a case such as this, we cannot use Mode as a measure of Central Tendency. For example, the set: 3, 6, 9, 12, 15, 18, 21, 24, 27, 20 does not have any number on repeat. Therefore, it does not have any mode.

Q. Is the formula of Mode the same for Grouped and Ungrouped Data? What is the formula of calculating mode?
Ans: No the formula for the calculation of mode is different in the two cases. The Mode of the Grouped Data can be found with the formula: Mode = L+h(fm−f1)(fm−f1)−(fm−f2).
Students should follow the below steps to find out the Mode of the Ungrouped Data:
– Arrange the data values in either ascending or descending order.
– Identify the values that have been repeated and the frequency of repeat.
– The value that has been repeated the maximum number of times is the mode of the given data.