Calculate Karl Pearson’s coefficient of correlation between X and Y for the following data:

In a trivariate distribution:

₁ = 2, ₂ = ₃ = 3, r₁₂ = 0.7, r₂₃ = r₃₁ = 0.5

Find (i) r_23.1 ,    (ii) R_1.23 , (iii) b_12.3 , b_13.2 and    (iv) _1.23

In a statistical study related to the price (in of two shares X and Y, the following two regression lines were found:

Y = 4X – 35 and 9X = Y + 135

The standard deviation of the price of Share Y is Rs12. You are required to calculate:

i) Average Price of shares X and Y

ii) Standard deviation of the price of Share X and

iii) Coefficient of correlation between the price of Shares X and Y.

Calculate the coefficient of rank correlation for the following data:

For the following frequency distribution of scores in Statistics of 50 students selected at random from among those appearing in a certain examination, compute the first four moments about mean:

Among the adult population of a certain town 50 percent are males, 60 percent are wage earners and 50 percent are 45 years of age or over, 10 percent of the males are not wageearners, and 40 per cent of the males are under 45 years. Make the best possible inference about the limits within which the percentage of persons (male or female) of 45 years or over are wage earners.

An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:
                                               Firm A                                Firm B

Number of Workers                    500                                   600

Average daily wage                      Rs. 186                            Rs. 175

Variance of Distribution of wages    81                                    100

i) Which firm A or B has a larger wage bill?

ii) In which firm, A or B, is there greater variability in individual wages?

iii) Calculate (a) the average daily wage, and (b) the variance of the distribution of wages of all the workers in the firms A and B taken together.