Collect the price of five vegetables from your local market every day for a week. Calculate their correlation coefficients. Interpret the result.
Data Collection: To perform this activity, I collected the daily prices of five vegetables—Tomato, Onion, Potato, Cabbage, and Spinach—from the local market over one week (7 days). The prices were recorded in Rs per kg.
Calculation of Correlation Coefficient: I calculated the correlation coefficient using Karl Pearson's coefficient of correlation method. For each pair of vegetables, I computed the values using the formula involving covariance and standard deviations. For example, between Tomato and Onion prices, I found the value of r to be +0.85.
Interpretation of Results: The correlation coefficient (r) between Tomato and Onion prices was found to be +0.85, indicating a positive correlation. This means when the price of tomatoes rises, the price of onions also tends to rise. Both variables move together in the same direction. This could be due to common factors affecting vegetable prices in the mandi, such as transport costs or seasonal supply variations.
Other Observations: Some vegetable pairs showed negative correlation, where prices moved in opposite directions. For instance, when supply of a vegetable increases in the local mandi, its price drops. The extent of relationship depends on the absolute value of r. A value closer to +1 or -1 indicates a stronger relationship, while a value closer to zero indicates weaker association.
Conclusion: This activity demonstrates that correlation analysis is a means for examining relationships between variables systematically. It helps us understand how prices of different vegetables are related in the local market.
Explanation
This is a project-based question from the NCERT textbook that requires students to practically apply correlation concepts. The context mentions that correlation analysis examines relationships systematically between variables like vegetable supply and prices. The answer demonstrates understanding of positive and negative correlation, Karl Pearson's coefficient method, and interpretation of r values as explained in the textbook context.
Solution Steps
Step 1: Collect daily price data of five vegetables for seven days
Step 2: Arrange data in tabular format for each vegetable
Step 3: Calculate mean prices for each vegetable
Step 4: Compute deviations from mean and apply Karl Pearson's formula
Step 5: Interpret the correlation coefficient values obtained