Understanding the University Entrance Exam Data

The question asks us to find the average of the difference between the number of candidates who appeared and the number of candidates who qualified for the B.Sc. stream over five different years (2016 to 2020).

The data is given in a table, where the numbers are in thousands. We need to calculate the difference (Appeared - Qualified) for B.Sc. for each year, sum these differences, and then find the average by dividing the sum by the number of years (which is 5).

Let's look at the B.Sc. data for each year:

• 2016: Appeared = 3.4 thousand, Qualified = 1.2 thousand
• 2017: Appeared = 3.6 thousand, Qualified = 1.8 thousand
• 2018: Appeared = 4.2 thousand, Qualified = 2.1 thousand
• 2019: Appeared = 4.8 thousand, Qualified = 2.3 thousand
• 2020: Appeared = 3.8 thousand, Qualified = 1.9 thousand

Calculating the Difference for B.Sc. Candidates Year-wise

We will calculate the difference between the Appeared (A) and Qualified (Q) candidates for the B.Sc. stream for each year.

• For 2016: Difference $= A - Q = 3.4 - 1.2 = 2.2$ thousand
• For 2017: Difference $= A - Q = 3.6 - 1.8 = 1.8$ thousand
• For 2018: Difference $= A - Q = 4.2 - 2.1 = 2.1$ thousand
• For 2019: Difference $= A - Q = 4.8 - 2.3 = 2.5$ thousand
• For 2020: Difference $= A - Q = 3.8 - 1.9 = 1.9$ thousand

We can put these differences into a table for clarity:

Calculating the Total Difference and Average Difference

Now, we need to find the total sum of these differences over the five years:

Total Difference $= 2.2 + 1.8 + 2.1 + 2.5 + 1.9 = 10.5$ thousand

To find the average difference, we divide the total difference by the number of years, which is 5.

Average Difference (in thousands) $= \frac{\text{Total Difference}}{\text{Number of Years}}$

Average Difference (in thousands) $= \frac{10.5}{5} = 2.1$ thousand

Converting Average Difference to Actual Number

Since the data in the table is in thousands, the average difference of 2.1 thousand needs to be converted to an actual number by multiplying by 1000.

Average Difference $= 2.1 \times 1000 = 2100$

Therefore, the average of the difference between total number of candidates who Appeared and the Qualified candidates for the stream B.Sc. for 2016-2020 is 2100.

Revision Table: Key Calculations

Additional Information on Data Analysis and Averages

This problem involves basic data interpretation from a table and calculating an average. Understanding how to read data presented in units (like 'thousands') is crucial.

• Data Interpretation: Carefully reading the table and understanding what each row and column represents is the first step. Pay attention to the units (e.g., thousands).
• Difference: Finding the difference between two numbers involves subtraction. In this case, it was Appeared minus Qualified candidates.
• Average: The average (or mean) of a set of numbers is calculated by summing all the numbers in the set and then dividing by the count of numbers in the set. The formula for the average is:

  $\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}$

• Working with Units: When data is given in specific units (like thousands), calculations can be done with those units, but the final answer must be converted to the required format (in this case, actual numbers).

Problems like this test your ability to perform simple arithmetic operations and interpret data presented in tables, which is common in many quantitative aptitude sections of exams.