Mode Calculation for Student Marks

This solution explains how to determine the mode from a list of marks obtained by students. The mode is a key concept in statistics representing the most frequent value.

Understanding the Mode

The mode is defined as the value that occurs most often in a data set. For example, in the set {2, 3, 3, 4, 5}, the mode is 3 because it appears twice, more than any other number.

Analyzing the Given Data

The marks scored by 10 students are provided as follows:

12, 14, 14, 15, 12, 16, 12, 10, 19, 11

Finding the Mode: Step-by-Step

1. List the Data Points: The first step is to list all the given marks: 10, 11, 12, 12, 12, 14, 14, 15, 16, 19.
2. Count Occurrences (Frequency): Next, we count how many times each distinct mark appears in the list. This is also known as finding the frequency of each value.
3. Create a Frequency Table: Organizing the counts in a table helps visualize the frequencies clearly.

   Marks	Frequency (Number of Students)
   10	1
   11	1
   12	3
   14	2
   15	1
   16	1
   19	1

   
   
4. Identify the Highest Frequency: Examine the 'Frequency' column to find the largest count. In this table, the highest frequency is 3.
5. Determine the Mode Value: The value associated with the highest frequency is the mode. The mark 12 appears 3 times, which is more than any other mark.

Conclusion on Mode

Based on the frequency count, the mark that appears most frequently in the data set is 12. Therefore, the mode of the given marks is 12.