Analyzing Student Sports Participation Data

The problem asks us to find the number of classes where more than 180 students like to play handball, based on the provided table showing class-wise student numbers and sports preferences percentages.

Understanding the Data Table

The table gives us two key pieces of information for each class (A through E):

1. The total number of students in the class.
2. The percentage of students in that class who like to play specific sports, including handball.

Calculating Students who Like Handball per Class

To find the actual number of students who like handball in each class, we need to calculate the given percentage of the total number of students in that class. The formula is:

Number of students liking Handball = (Total students in class) $\times$ (Percentage liking Handball / 100)

• Class A: Number of students liking handball = $240 \times \frac{50}{100} = 240 \times 0.50 = 120$.
• Class B: Number of students liking handball = $280 \times \frac{60}{100} = 280 \times 0.60 = 168$.
• Class C: Number of students liking handball = $320 \times \frac{55}{100} = 320 \times 0.55 = 176$.
• Class D: Number of students liking handball = $360 \times \frac{65}{100} = 360 \times 0.65 = 234$.
• Class E: Number of students liking handball = $480 \times \frac{75}{100} = 480 \times 0.75 = 360$.

Comparing with 180 Students

Now we compare the number of students who like handball in each class with 180 to see if it is more than 180.

• Class A: 120 students. Is $120 > 180$? No.
• Class B: 168 students. Is $168 > 180$? No.
• Class C: 176 students. Is $176 > 180$? No.
• Class D: 234 students. Is $234 > 180$? Yes.
• Class E: 360 students. Is $360 > 180$? Yes.

Determining the Value of M

The question defines M as the number of classes in which more than 180 students like to play handball. Based on our comparison, the classes where more than 180 students like handball are Class D and Class E.

There are 2 such classes.

Therefore, M = 2.

Final Answer

The number of classes in which more than 180 students like to play handball is 2. So, M = 2.

Revision Table: Handball Participation Summary

Additional Information: Data Interpretation Skills

Interpreting data from tables like this is a common skill tested in many exams. It involves extracting relevant information, performing calculations (like percentages), and comparing values to answer specific questions. Key aspects include:

• Carefully reading the column and row headers to understand what the numbers represent.
• Identifying the specific data points needed for the calculation (e.g., total students in a class and the percentage for a specific sport).
• Knowing how to convert percentages to decimal form or fractions for calculation.
• Performing the required arithmetic accurately.
• Comparing the results against a given threshold or condition, as required by the question.
• Keeping track of which classes meet the specified condition to count them for the final answer.

These skills are fundamental for data analysis and quantitative reasoning.