Finding the Difference in Average Qualified Candidates (M.Sc. vs MA, 2016-2020)

The question asks us to find the difference between the average number of qualified candidates for M.Sc. and MA courses over the period from 2016 to 2020, based on the data provided in the table.

Understanding the University Entrance Examination Data Table

The table presents the number of candidates who appeared (A) and qualified (Q) for a university entrance examination across different courses (BSc, BA, MSc, MA) for five years (2016 to 2020). The values are given in thousands.

We need to focus on the 'Qualified' (Q) column for M.Sc. and MA for the years 2016 through 2020.

Step-by-Step Calculation

1. Calculate the Total Qualified Candidates for M.Sc. (2016-2020):

Sum the 'Q' values for M.Sc. from 2016 to 2020:

Total M.Sc. Qualified $= 1.3 + 1.1 + 1.2 + 1.2 + 1.3$ thousand

Total M.Sc. Qualified $= 6.1$ thousand

2. Calculate the Average Qualified Candidates for M.Sc. (2016-2020):

The average is the total sum divided by the number of years (which is 5).

Average M.Sc. Qualified $= \frac{\text{Total M.Sc. Qualified}}{\text{Number of Years}}$

Average M.Sc. Qualified $= \frac{6.1}{5}$ thousand

Average M.Sc. Qualified $= 1.22$ thousand

3. Calculate the Total Qualified Candidates for MA (2016-2020):

Sum the 'Q' values for MA from 2016 to 2020:

Total MA Qualified $= 2.4 + 2.3 + 2.5 + 2.7 + 3.2$ thousand

Total MA Qualified $= 13.1$ thousand

4. Calculate the Average Qualified Candidates for MA (2016-2020):

Average MA Qualified $= \frac{\text{Total MA Qualified}}{\text{Number of Years}}$

Average MA Qualified $= \frac{13.1}{5}$ thousand

Average MA Qualified $= 2.62$ thousand

5. Calculate the Difference Between the Averages:

Difference $= \text{Average MA Qualified} - \text{Average M.Sc. Qualified}$

Difference $= 2.62 - 1.22$ thousand

Difference $= 1.40$ thousand

6. Convert the Difference to Actual Numbers:

Since the values in the table are in thousands, we multiply the difference by 1000.

Difference in actual numbers $= 1.40 \times 1000$

Difference in actual numbers $= 1400$

Conclusion

The difference between the average number of qualified candidates for M.Sc. and MA from 2016 to 2020 is 1400.

Revision Table: Key Data Points

Additional Information: Understanding Averages in Data Analysis

The average (or mean) is a common measure used in data analysis to find a typical value within a dataset. It is calculated by summing all the values in the dataset and dividing by the number of values. In the context of this university entrance examination data, calculating the average number of qualified candidates over several years helps us understand the general trend or performance level for a specific course over that period, smoothing out year-to-year fluctuations. Comparing the averages between different courses like M.Sc. and MA allows for a direct comparison of their performance relative to each other over the same timeframe.

• An average provides a single value that represents the center of a dataset.
• Calculating averages over a period helps identify long-term trends rather than focusing on individual year anomalies.
• Comparing averages of different categories allows for insightful comparisons based on typical performance.