Finding the Largest Difference in Student Numbers

The question asks us to find the interval where the difference between the number of students studying Physics and Mathematics is the largest. We are given a table showing the number of students in different mark ranges for both subjects.

To solve this, we need to calculate the absolute difference in the number of students for Physics and Mathematics for each given interval. The absolute difference means we consider the magnitude of the difference, regardless of which subject has more students.

Let's list the data from the table:

Calculating the Difference in Students per Interval

Now, we calculate the absolute difference for each interval:

• For the interval 10 – 20: Difference = \(\left| \text{Number of students in Physics} - \text{Number of students in Mathematics} \right| = \left| 8 - 10 \right| = \left| -2 \right| = 2\)
• For the interval 20 – 30: Difference = \(\left| 11 - 21 \right| = \left| -10 \right| = 10\)
• For the interval 30 – 40: Difference = \(\left| 30 - 38 \right| = \left| -8 \right| = 8\)
• For the interval 40 – 50: Difference = \(\left| 26 - 15 \right| = \left| 11 \right| = 11\)
• For the interval 50 – 60: Difference = \(\left| 15 - 10 \right| = \left| 5 \right| = 5\)
• For the interval 60 - 70: Difference = \(\left| 10 - 6 \right| = \left| 4 \right| = 4\)

Comparing Differences to Find the Largest

Let's list the calculated differences for each interval:

• 10 – 20: 2
• 20 – 30: 10
• 30 – 40: 8
• 40 – 50: 11
• 50 – 60: 5
• 60 - 70: 4

Comparing these values (2, 10, 8, 11, 5, 4), the largest difference is 11.

Identifying the Interval with the Largest Difference

The largest difference, 11, occurs in the interval 40 – 50.

Therefore, the difference between the number of students under Physics and Mathematics is largest for the interval 40 - 50.

Revision Table: Student Data Analysis

As shown in the table, the maximum absolute difference is 11, which corresponds to the 40 - 50 marks interval.

Additional Information: Understanding Frequency Tables

A frequency table is a table that lists items and shows the number of times the items occur. In this case, the items are the mark intervals, and the frequency is the number of students falling into each interval for Physics and Mathematics separately.

• Intervals: These are ranges of values (like 10-20, 20-30, etc.). They help organize data into manageable groups.
• Frequency: The count of how many data points (students in this case) fall within a specific interval.
• Analyzing Differences: Comparing frequencies across categories (like Physics vs. Mathematics) within the same interval helps identify where the distributions of data differ most significantly. This type of analysis is useful in various fields, including education, to understand variations.