If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.

Mean and Standard deviation of 18 observations are found to be 7 and 4, respectively. On comparing the original data, it was found that an observation 12 was miscopied as 21 in the calculations. Calculate correct mean and standard deviation.

State whether the following statements are True or False and also give the reason in support of your answer.
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.

A researcher collects the following information for two variables x and y:
 n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, σ_x = 4 and σ_y = 5
 Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y).

The frequency distribution of the marks obtained by the 25 students each of the two sections is given as follows:

Find the missing information from the following data:

Board of Directors of Labour Union wishes to sample the opinion of its members before submitting a change in its contribution at a forthcoming annual meeting. Questionnaires are sent to a random sample of 200 members in three union locals. The results of the survey are as follows: