How will this question be solved?

• Total Students (n): 100
• Median Package: ₹6 LPA

Because 100 is an even number, the median is calculated as the average of the two middle terms: the 50th and the 51st students in the sorted list.

To find how many students must have received less than ₹6 LPA, we look at the positions in our sorted list:

The 51st student and above: Since the median is 6, the 51st student must have a value greater than equal to 6 LPA

The 50th student and below: For the average of the 50th and 51st positions to be 6, there are a few possibilities for the 50th student:

• If the 50th and 51st students both got exactly ₹6 LPA, the median is 6.
• If the 51st student got more than ₹6 LPA (e.g., ₹6.5 LPA), the 50th student must have received less than ₹6 LPA (e.g., ₹5.5 LPA) to balance the average to 6.
• In a batch of 100, exactly 50 students (the bottom half) represent the values at or below the median threshold.However, for the median to be ₹6 LPA, we cannot have more than 50 students earning less than ₹6 LPA. If the 50th student also earned less than ₹6 LPA, and the 51st student earned ₹6 LPA or more, the median would only be ₹6 LPA if their average hit that mark. By standard definition for a batch of 100:At least 50 students must have received ₹6 LPA or more.
• At least 50 students must have received ₹6 LPA or less.

Therefore, the maximum number of students who could have received strictly less than ₹6 LPA is 49, assuming the 50th student received exactly ₹6 LPA. If the 50th student received less than ₹6 LPA, then the 51st student must have received more than ₹6 LPA to maintain the average of 6.

Hence, at most 50 students received ₹6 LPA or less.