Question

find the karl pearsons coeffecient of correlation between the proce and the quantity demanded from the following data 5,10,15,20,25

Answer 1

To find the Karl Pearson's coefficient of correlation between the price and the quantity demanded, we need to calculate the correlation coefficient using the given data. The Karl Pearson's coefficient of correlation between the price and the quantity demanded is 1.

Step-by-step explanation:

To find the Karl Pearson's coefficient of correlation between the price and the quantity demanded, we need to calculate the correlation coefficient using the given data: 5, 10, 15, 20, 25.

1. First, find the mean of both the price and the quantity demanded: mean_price = (5 + 10 + 15 + 20 + 25) / 5 = 15 and mean_quantity = (5 + 10 + 15 + 20 + 25) / 5 = 15.
2. Next, calculate the deviations from the mean for each data point: price_deviations = {5 - 15, 10 - 15, 15 - 15, 20 - 15, 25 - 15} = {-10, -5, 0, 5, 10} and quantity_deviations = {5 - 15, 10 - 15, 15 - 15, 20 - 15, 25 - 15} = {-10, -5, 0, 5, 10}.
3. Then, calculate the sum of the products of the deviations: sum_products = (-10 * -10) + (-5 * -5) + (0 * 0) + (5 * 5) + (10 * 10) = 150.
4. Finally, calculate the standard deviations of price and quantity demanded:

• standard_deviation_price = sqrt(((-10 * -10) + (-5 * -5) + (0 * 0) + (5 * 5) + (10 * 10)) / 5) = 7.746.
• standard_deviation_quantity = sqrt(((-10 * -10) + (-5 * -5) + (0 * 0) + (5 * 5) + (10 * 10)) / 5) = 7.746.

Now, calculate the correlation coefficient using the formula: r = (sum_products) / (standard_deviation_price * standard_deviation_quantity) = 150 / (7.746 * 7.746) = 1.

The Karl Pearson's coefficient of correlation between the price and the quantity demanded is 1.