Understanding the Question on Average Vacant Seats

The question asks for the difference between the average number of vacant seats in the BTech course and the average number of vacant seats in the MTech course over a period of five years, from 2016 to 2020. To find this difference, we first need to calculate the number of vacant seats for each course in each year, then find the average number of vacant seats for each course over the five years, and finally calculate the difference between these averages.

Calculating Vacant Seats per Year

The number of vacant seats in a course for a given year is calculated by subtracting the number of enrolled students from the maximum number of seats available for that course.

Vacant Seats = Maximum Seats - Enrolled Students

From the table, we know:

• Maximum seats in BTech: 60
• Maximum seats in MTech: 30

Let's calculate the vacant seats for BTech and MTech for each year from 2016 to 2020:

Calculating Total and Average Vacant Seats

Now, we sum the vacant seats for each course over the five years (2016-2020) to find the total vacant seats.

• Total Vacant Seats in BTech = \(15 + 5 + 12 + 7 + 10 = 49\)
• Total Vacant Seats in MTech = \(5 + 4 + 9 + 7 + 2 = 27\)

Next, we calculate the average vacant seats for each course by dividing the total vacant seats by the number of years, which is 5.

• Average Vacant Seats in BTech = \(\frac{\text{Total BTech Vacant Seats}}{\text{Number of Years}} = \frac{49}{5} = 9.8\)
• Average Vacant Seats in MTech = \(\frac{\text{Total MTech Vacant Seats}}{\text{Number of Years}} = \frac{27}{5} = 5.4\)

Calculating the Difference in Average Vacant Seats

Finally, we find the difference between the average vacant seats in BTech and the average vacant seats in MTech.

Difference = Average Vacant Seats (BTech) - Average Vacant Seats (MTech)

Difference = \(9.8 - 5.4 = 4.4\)

The difference between the average vacant seats in BTech and MTech during 2016-2020 is 4.4.

Step-by-Step Summary

1. Identify maximum seats for BTech (60) and MTech (30).
2. Calculate vacant seats for BTech in each year (2016-2020) by subtracting enrollment from 60.
3. Calculate vacant seats for MTech in each year (2016-2020) by subtracting enrollment from 30.
4. Sum vacant seats for BTech over the 5 years.
5. Sum vacant seats for MTech over the 5 years.
6. Calculate the average vacant seats for BTech by dividing the sum by 5.
7. Calculate the average vacant seats for MTech by dividing the sum by 5.
8. Find the difference between the average vacant seats of BTech and MTech.

Revision Table: Key Calculations for Vacant Seats Difference

Additional Information: Understanding Averages and Data Analysis

An average (specifically, the arithmetic mean) is a measure of central tendency. It gives us a single value that represents the typical value in a set of numbers. In this problem, calculating the average vacant seats for BTech and MTech helps us compare the overall trend of empty seats in these courses over the five-year period, rather than focusing on individual year fluctuations. This type of data analysis is common in studying trends in enrollment, capacity utilization, and resource allocation in educational institutions.

The difference between averages highlights which course, on average, had more unused capacity during the given timeframe. A larger difference indicates a more significant disparity in how close the courses came to reaching their maximum enrollment capacity.