Appendix 2: Mathematical Modelling | A2.3

Question 1

Based upon the data of the past five years, try and forecast the average percentage of marks in Mathematics that your school would obtain in the Class X board examination at the end of the year.

Solution

Understand the Question

To forecast future performance using mathematical modelling, we calculate the arithmetic mean (average) of past data.
If actual school records are not readily available, representative sample data for the past 5 years can be assumed.
The forecasted percentage is obtained by finding the sum of percentages over the 5 years and dividing by $5$ . $\text{Forecasted Average} = \dfrac{\text{Sum of marks/percentages of past 5 years}}{5}$

Step 1 · Assume or Collect Data for Past Five Years

Let the average percentage of marks obtained in Mathematics by the school in the past five years be:

Year 1: $78\%$
Year 2: $80\%$
Year 3: $79\%$
Year 4: $82\%$
Year 5: $81\%$

Step 2 · Calculate the Average Percentage

\begin{aligned} \text{Average percentage} &= \dfrac{78 + 80 + 79 + 82 + 81}{5} \\[0.6em] &= \dfrac{400}{5} \\[0.6em] &= 80\% \end{aligned}

Answer

$80\%$

Common Mistakes

Open-Ended Nature: This is a mathematical modelling question, so the exact answer depends on the specific dataset collected or assumed for the school.
Divisor Error: Forgetting to divide by the total number of years ( $5$ ) after summing the past values.