Analyzing Student Performance Data

The problem requires us to analyze the given table showing the percentage of marks obtained by 7 students across 5 subjects. Since the maximum marks in each subject is 100, the percentage directly represents the marks obtained by the student in that subject.

The goal is to find the ratio between the student with the highest total marks and the student with the lowest total marks.

Understanding the Data Table

Here is the provided data table showing marks (out of 100) for each student in each subject:

Calculating Total Marks for Each Student

To find the total marks for each student, we need to sum the marks obtained in all 5 subjects for that student.

• Student 1 Total Marks: $40 + 45 + 55 + 65 + 70 = 275$
• Student 2 Total Marks: $60 + 70 + 75 + 65 + 60 = 330$
• Student 3 Total Marks: $70 + 74 + 64 + 68 + 72 = 348$
• Student 4 Total Marks: $50 + 75 + 57 + 65 + 62 = 309$
• Student 5 Total Marks: $61 + 66 + 72 + 58 + 60 = 317$
• Student 6 Total Marks: $70 + 65 + 68 + 56 + 78 = 337$
• Student 7 Total Marks: $65 + 45 + 70 + 52 + 58 = 290$

Identifying Highest and Lowest Total Marks

Now, we compare the total marks obtained by all 7 students to find the highest and the lowest totals.

• Total Marks: 275, 330, 348, 309, 317, 337, 290

From this list:

• The highest total marks is 348 (obtained by Student 3).
• The lowest total marks is 275 (obtained by Student 1).

Calculating the Required Ratio

The question asks for the ratio between the student having the highest total marks and the student having the lowest total marks. This is calculated as:

$\text{Ratio} = \frac{\text{Highest Total Marks}}{\text{Lowest Total Marks}}$

Using the values we found:

$\text{Ratio} = \frac{348}{275}$

This fraction cannot be simplified further as 348 and 275 share no common factors other than 1.

Final Answer Derivation

The ratio between the student having the highest total marks and the student having the lowest total marks is $\frac{348}{275}$.

Revision Table: Key Calculations

• Highest Total: 348 (Student 3)
• Lowest Total: 275 (Student 1)
• Ratio: $\frac{348}{275}$

Additional Information: Data Interpretation Basics

This problem involves basic data interpretation from a table. Here are some related concepts:

• Summation: Adding up values across categories (subjects for a student).
• Comparison: Finding the maximum and minimum values in a set of numbers.
• Ratio: A comparison of two quantities by division. Ratios can be expressed as fractions (a/b) or using a colon (a:b). Simplifying ratios often helps in comparing them, but in this case, the fraction is already in simplest form.
• Percentage Marks: When maximum marks are 100, percentage marks directly represent the marks obtained. If the maximum marks were different (e.g., 50), the percentage would need to be converted to actual marks ($(\text{Percentage}/100) \times \text{Maximum Marks}$).
• Data Analysis: The process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. This problem is a simple form of data analysis.