Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
and
Karl Pearson's coefficient of correlation (\( r \)) is given by the formula: \[ r = \frac{N\sum XY - _____ __________ ___ _________ _______ _______ ________ __________ ___.
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State whether the following statements are true or false and also give the reason in support of your answer:
(a) if are the variate values of two variables X and and their geometric means are Grand G₂, respectively, then geometric mean of
will be (G1/G2).
(b) If X and Y are two independent variables and the variables U=X+ Y and V= X-Y, then the
(c) If each value of X is divided by 2 and of Y is multiplied by 2, then b'yx will be same as byx.
(d) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.
(e) If
50% of items have characteristics A and B both, 35% have A, but not B, 25% have B but not A. Show that there must be some misprints in this report.
In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as 8X - 10Y + 70 = 0 and 20X - 9Y - 65 = 0. The standard deviation of X = 3, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y
The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.
An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 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 graduate. Obtain all the ultimate class frequencies.
Given the following data:
(i) r12.3 (ii) r13.2(iii) r 23.1 (iv) R1.23
Can vaccination be regarded as a preventive measure for smallpox from the given data:
(i) Of 1482 persons in a locality exposed to smallpox, 368 in all were attacked, and
(ii) Of 1482 persons, 343 had been vaccinated and of these only 35 were attacked.