Understanding the Enrollment Data Table

The question asks us to find the difference between the average student enrollment in the year 2016 and the average student enrollment in the year 2017. The provided table shows the enrollment numbers for five different courses over several years. To solve this, we need to calculate the total enrollment for each year and then find the average enrollment for each year. Finally, we calculate the difference between these averages.

Calculating Total Enrollment in 2016

To find the total enrollment in 2016, we sum the enrollments for all five courses in that year:

• BTech enrollment in 2016: 45
• MCA enrollment in 2016: 52
• MTech enrollment in 2016: 25
• MPhil enrollment in 2016: 16
• Integrated MTech enrollment in 2016: 26

Total enrollment in 2016 = $45 + 52 + 25 + 16 + 26 = 164$

Calculating Average Enrollment in 2016

The average enrollment in 2016 is the total enrollment divided by the number of courses, which is 5.

Average enrollment in 2016 = $\frac{\text{Total enrollment in 2016}}{\text{Number of courses}}$

Average enrollment in 2016 = $\frac{164}{5} = 32.8$

Calculating Total Enrollment in 2017

Next, we find the total enrollment in 2017 by summing the enrollments for all five courses in 2017:

• BTech enrollment in 2017: 55
• MCA enrollment in 2017: 56
• MTech enrollment in 2017: 26
• MPhil enrollment in 2017: 18
• Integrated MTech enrollment in 2017: 24

Total enrollment in 2017 = $55 + 56 + 26 + 18 + 24 = 179$

Calculating Average Enrollment in 2017

The average enrollment in 2017 is the total enrollment divided by the number of courses, which is 5.

Average enrollment in 2017 = $\frac{\text{Total enrollment in 2017}}{\text{Number of courses}}$

Average enrollment in 2017 = $\frac{179}{5} = 35.8$

Finding the Difference in Average Enrollment

Finally, we find the difference between the average enrollment in 2016 and the average enrollment in 2017. We are looking for the absolute difference.

Difference = $| \text{Average enrollment in 2017} - \text{Average enrollment in 2016} |$

Difference = $| 35.8 - 32.8 |$

Difference = $| 3.0 |$

Difference = $3.0$

The difference between the average enrollment in 2016 and the average enrollment in 2017 is 3.0.

Revision Table: Enrollment Calculations

Difference in Averages = $|35.8 - 32.8| = 3.0$

Additional Information: Understanding Averages

The average, also known as the arithmetic mean, is a common measure used to represent a set of numbers. It is calculated by summing all the values in the set and then dividing by the number of values in the set. In this problem, we calculated the average enrollment for a year by summing the enrollment across different courses for that year and dividing by the number of courses. Averages help in understanding the central tendency or typical value within a dataset. Comparing averages over different periods, as done here between 2016 and 2017 average enrollments, helps in identifying trends or changes in the data. Data interpretation questions often involve calculating averages, percentages, ratios, or differences based on given tables or charts.