An investigation of 23,713 households was made in an urban and rual mixed locality. Of these 1,618 were farmers, 2,015 well-to-do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well-to-do, also 587 well-to-do families were those of farmers and out of them only 156 were having at least one of their family member as graduate. Obtain all the ultimate class frequencies

The mean and the standard deviation of a characteristic of 100 items were found to be 60 and 10 respectively. At the time of calculations, two items were wrongly taken as 5 and 45 instead of 30 and 20. Calculate the corrected mean and corrected standard deviation.

Investigate the association between darkness of eye-colour in father and son from the following data:

Fathers with dark eyes and sons with dark eyes: 50

Fathers with dark eyes and sons with not dark eyes: 79

Fathers with not dark eyes and sons with dark eyes: 89

Fathers with not dark eyes and sons with not dark eyes: 782

Also tabulate for comparison the frequencies that would have been observed had there been no heredity.

The following table gives, according to age, the frequency of marks obtained by 100 students in an intelligence test:

If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated

If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.

Calculate the first four moments of the following distribution about the mean and hence find β1 and β2.