Hey, everyone, welcome back! In today’s blog post, we will tackle a problem encountered in a recent maths exam for 25 students. The problem revolves around calculating the mean mark before and after certain modifications to the students’ scores. This scenario helps us understand how changes in data affect the mean, a fundamental concept in statistics.
Understanding the Problem
Let’s start by breaking down the question from the exam. There are 25 students, and their mean exam score is 83 marks. Now, the examiner decides to adjust some of the scores:
- Five additional marks are awarded to nine students.
- Two marks are deducted from ten students.
Our task is to determine the new mean score after these adjustments.
Calculating the Total Marks
First, we need to find the total marks initially obtained by the 25 students. We know the mean score is 83. Hence, the total marks can be calculated as:
[\text{Total Marks} = \text{Mean} \times \text{Number of Students} = 83 \times 25]
[\text{Total Marks} = 2075]
So, the original total marks for the 25 students is 2075.
Adjusting the Marks
Next, let’s account for the changes made by the examiner. There are additions and subtractions to consider.
Addition of Marks
The examiner awards 5 additional marks to 9 students:
[5 \text{ marks} \times 9 \text{ students} = 45 \text{ additional marks}]
Subtraction of Marks
The examiner deducts 2 marks from 10 students:
[2 \text{ marks} \times 10 \text{ students} = 20 \text{ marks deducted}]
Net Change
To get the net change in total marks, we subtract the deducted marks from the additional marks:
[45 \text{ additional marks} – 20 \text{ marks deducted} = 25 \text{ net additional marks}]
New Total Marks
Now, we add this net change to the original total marks:
[2075 + 25 = 2100]
So, the new total marks for the 25 students are 2100.
Calculating the New Mean
To find the new mean score after these adjustments, we divide the new total marks by the number of students:
[\text{New Mean} = \frac{2100}{25}]
[\text{New Mean} = 84]
Thus, the new mean mark for the 25 students is 84.
“Mean questions are typically quite simple, but when there’s more problem-solving involved, always focus on calculating the total marks first.” – Exam Tip
Summary
Let’s summarise our steps for clarity:
- Initial Total Marks: Multiply the mean score by the number of students to get the initial total marks.
- Adjustments: Calculate the total additional marks and total deducted marks.
- Net Change: Determine the net change by subtracting the deductions from the additions.
- New Total Marks: Add the net change to the initial total marks.
- New Mean: Divide the new total marks by the number of students to get the new mean.
Remember, understanding how to manipulate and adjust data is crucial in many statistical problems. These steps can be applied to various scenarios, whether in exams, real-world data analysis, or research.
Visual Representation
Step-by-Step Calculations
Initial Mean = 83Number of Students = 25Total Marks = 83 * 25 = 2075Additional Marks:5 marks * 9 students = 45 marksMarks Deducted:2 marks * 10 students = 20 marksNet change in marks = 45 - 20 = 25New Total Marks = 2075 + 25 = 2100New Mean = 2100 / 25 = 84Visual Aids
[\text{Insert images or diagrams here to illustrate the steps visually. Example: images of the calculations, graphical representations of mean changes, etc.}]
Conclusion
In this blog post, we mastered calculating the mean after adjustments, a key skill in tackling statistical questions. By systematically breaking down the problem, calculating totals, and understanding the effects of changes, we simplified a seemingly complex problem into manageable steps. Keep practising these techniques to ace similar questions with ease.
Thanks for joining us, and stay tuned for more problem-solving tips and strategies!
Happy Studying!
If you have any comments or questions, feel free to leave them below. Also, check out our other blog posts for more exam tips and mathematical insights.