Question 3 of 3intermediate✨ CreateLong Answer5 marks

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.

Correct Answer

To forecast the average percentage of marks in Mathematics for the Class X board examination, we need to apply the process of mathematical modelling.

Step 1 (Understanding the problem): The real problem is to predict the average percentage of marks in Mathematics that our school would obtain. We need to collect data of the average percentages secured by Class X students in Mathematics for the past five years. We make an assumption that the conditions affecting performance remain similar and that the past data is a good representative for prediction.

Step 2 (Mathematical description): We translate the problem mathematically by representing the past five years' data. Let the average percentages be x1,x2,x3,x4,x5x_1, x_2, x_3, x_4, x_5. We can find the mean of these values. We may also observe if there is an increasing or decreasing trend.

Step 3 (Solving the mathematical problem): Calculate the mean percentage:

x1+x2+x3+x4+x55\frac{x_1 + x_2 + x_3 + x_4 + x_5}{5}

If a trend is observed (like a steady increase), we may adjust the forecast accordingly.

Step 4 (Interpreting the solution): The calculated mean gives us an estimate of the expected average percentage for the current year. This forecast helps the school anticipate performance, similar to how exit polls predict election results.

Step 5 (Validation): The forecast should be validated by comparing with actual results after the examination to improve future predictions.

Exercise: EXERCISE A2.3 | Q: 1 | (Page Page 11)
For More Understanding

Explanation

This question is from Exercise A2.3 which focuses on applying mathematical modelling to real-world problems. The textbook context outlines the stages of mathematical modelling: Step 1 (Understanding the problem), Step 2 (Mathematical description), Step 3 (Solving the mathematical problem), Step 4 (Interpreting the solution). The answer follows this structured approach.

The context also mentions estimation examples like exit polls predicting election results, which is analogous to forecasting examination results based on past data.

The key concept is that mathematical modelling helps solve real-world problems by simplifying them through assumptions and using mathematical techniques to arrive at solutions that can be interpreted in the context of the original problem.

Solution Steps

  1. Step 1: Understand the problem — define the real problem of forecasting marks based on past data.

  2. Step 2: Mathematical description — represent past five years' data mathematically.

  3. Step 3: Solve — calculate mean and observe trends.

  4. Step 4: Interpret — relate the mathematical solution to the real-world situation.

  5. Step 5: Validate — compare forecast with actual results.

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