Mode

What is a mode?

Mode is the value or number that occurs most frequently in a set of data. The value of mode provides an idea about the data set that appears the most. For example, out of several courses in a college, we can find out the course with the maximum number of registrations. Therefore, the mode formula gives us an idea about the most popular course in the college.

There are a lot of real-life applications where finding the average will not work. In the above example, finding the average number of students won’t tell us about the popularity of a particular course. We need the modal value for the same.

A mode in statistics

Mode is the value that appears the most number of times in a set of data. However, there is a possibility of a dataset not having any modal value. If there are repeated values, there can also be multiple modes. We can find a dataset with only one mode, multiple modes, or no modes. Depending on the number of modes, a dataset can be categorised into unimodal, bimodal, trimodal, or multimodal.

Mode Formula in Statistics

The mode formula in statistics is used to find the modal value or the frequently occurring value in a given set. The value which has the highest frequency is the mode of the dataset. Mode is a part of the three measures of central tendency along with mean and median. 

The mode formula in class 10 for ungrouped data is found by arranging the values in a list. The modal class is the data interval with the highest frequency after the arrangement. Now, the modal class has a lower limit which is L, ‘h’ the magnitude of class mark, ‘fm’ is the frequency of the modal class, f1 is the frequency of the class preceding the modal class, and f2 is the frequency of the class succeeding the modal class. Therefore, the mode formula is given by:

Mode = L + h [(fs- f1) / (fs- f1) + (fs- f2)

Mode Formula – Ungrouped Data 

The mode formula in statistics for ungrouped data can be simply found by arranging the data in ascending or descending order. The class interval or the observation with the highest frequency will be the modal value in the mode formula.

Mode Formula – Grouped Data

The mode formula for group data is the same as ungrouped data. The mode formula in class 10 is given as

Mode = L+ h(fs−f1) / (fs−f1)+(fs−f2) where,

The above mode formula in statistics is also written in another form, which is given by:

Mode = li+ hi [ (f1 – fo)/(2f1 – fo – f2)]

The variables mentioned in the two formulas above correspond to the class intervals in the modal class and the frequencies in the dataset are paramount to finding the mode. 

How to Find the Mode?

Depending on the type of data given, you have a mode formula in class 10 to help you find mode. A grouped data is shown in intervals or a graph. An ungrouped data will be shown to you in the form of a table. 

Ungrouped Data

The completely arbitrary data not displayed in groups is termed ungrouped data. We will take the example of a shoe store with different shoe sizes to find the mode.

From the above table; we can notice that shoe size 8 has the highest frequency; therefore, it is the mode of the given dataset. However, finding mode is a little complicated for Grouped data.

Grouped Data

Let us take an example of the scores of students in a particular examination.

The class interval with the highest frequency is the modal class; therefore, the modal class is 10-15. The lower limit or L of the modal class is 10, the fs here is 7, frequency of the class before 10-15 (f1) is 3, frequency of the class after 10-15 is 2, and the magnitude of the class (h) is 5. We have to substitute the values in the mode formula to find the value. In this dataset, the value of mode after substituting the figures will come to 12.22 which is the final modal value.

Conclusion

The mode can also be equal to mean and median, and it can also be found for a dataset with no repeating numbers. For ungrouped data, simple observation can help you find the mode.