Question 14 of 19advanced🔧 ApplyLong Answer5 marks

Measure the height of your classmates. Ask them the height of their benchmate. Calculate the correlation coefficient of these two variables. Interpret the result.

Correct Answer

To solve this question, we need to collect primary data and calculate the correlation coefficient.

Step 1: Data Collection Measure the height of each classmate (Variable X) and record the height of their benchmate (Variable Y). Prepare a table with columns for X, Y, and calculated values.

Step 2: Calculate Karl Pearson's Coefficient of Correlation Use the formula for Karl Pearson's Coefficient of Correlation, which gives a precise numerical value of the degree of linear relationship between two variables X and Y. Calculate the mean of X and Y, then find deviations from mean, their squares, and the product of deviations.

Step 3: Interpretation of Result After calculation, if the value of r is close to 1, it indicates a strong positive correlation, meaning taller students tend to have taller benchmates. If r is close to -1, it shows a strong negative correlation. If r is close to 0, there is no linear relationship between the heights of students and their benchmates.

Conclusion Since benchmates are assigned randomly (not based on height), the expected result would be r ≈\approx 0, indicating no significant correlation between the heights of classmates and their benchmates. This shows that seating arrangements in classrooms are typically independent of physical attributes like height.

Exercise: EXERCISES | Q: 14 | (Page 15)
For More Understanding

Explanation

This is a practical activity question from the NCERT textbook that requires students to apply Karl Pearson's correlation coefficient method. The question tests understanding of data collection, calculation methodology, and interpretation of correlation values. The context mentions that Karl Pearson's Coefficient gives a precise numerical value of the degree of linear relationship between two variables. Students are expected to understand that random benchmate assignment would typically result in near-zero correlation.

Solution Steps

  1. Step 1: Collect height data of classmates (X) and their benchmates (Y)

  2. Step 2: Create a table with X, Y, deviations, squares, and products

  3. Step 3: Apply Karl Pearson's correlation coefficient formula

  4. Step 4: Calculate the value of r

  5. Step 5: Interpret the result based on the value obtained (1, -1, or 0)

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