Finding the Mean Marks of the Third Group: An SEO-Friendly Guide

Understanding how to calculate the mean marks of groups is a critical skill for educators and students alike. This article delves into the steps and methods required to determine the mean marks of the third group, given specific data points. By following the detailed explanation, you will be well-prepared to solve similar problems efficiently.

Introduction

Statistical calculations play a vital role in analyzing student performance. In this scenario, we are given data on three groups of students and their mean marks. Our goal is to find the mean marks of the third group using the provided figures.

Given Data

Group 1: 25 students, mean 60 Group 2: 50 students, mean 55 Group 3: 25 students, mean unknown (x) Combined mean of all three groups: 58

Step-by-Step Calculation

Step 1: Calculate the Total Marks for Each Group

We start by calculating the total marks for each of the first two groups:

Total marks of Group 1  25 students times; 60 marks/student  1500

Total marks of Group 2  50 students times; 55 marks/student  2750

Step 2: Calculate the Total Number of Students and the Total Marks

Determining the total number of students and the combined total marks is crucial for our calculations:

Total number of students  25   50   25  100 students

Combined total marks  100 students times; 58 marks/student  5800

Step 3: Set Up the Equation for Total Marks

To find the total marks of Group 3, we can use the combined mean of all three groups:

1500   2750   25x  5800

Step 4: Simplify and Solve for x

By solving the equation, we can determine the mean marks of Group 3:

4250   25x  5800

25x  5800 - 4250

25x  1550

x  1550 / 25  62

Conclusion

The mean of the marks scored by the third group is 62.

Additional Insights

Understanding the concept of combined means can be particularly useful in various real-world scenarios. For instance, when combining data from multiple tests or group assessments, it is essential to account for the size of each group. The following are some key takeaways:

The combined mean is a weighted average that considers the size and the mean values of each group. Using this method, you can efficiently analyze large datasets and derive meaningful conclusions. Making use of statistical methods can help in making informed decisions and identifying areas of improvement.

By mastering the techniques outlined in this article, you can apply these concepts to similar problems and enhance your statistical analysis skills.

Related Keywords

Mean marks Group statistics Combined mean Student scores