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
(a) False.
The geometric mean of the ratio \( X/Y \) is not necessarily \( G_1/G_2 \). The geometric mean of a ratio is given by the ratio of the geometric means only if the values of \( X \) and \( Y \) are perfectly proportional, which is not always the case.
(b) False. _______ __________ ______ ________ ___ ___ ______ ______ _____ __________ ____.
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Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
and
Suppose X and Y are the two variables having the correlation coefficient 0.85. The following are the values they have:
| X | Y |
| 10 | 40 |
| 30 | 30 |
| 50 | 70 |
| 60 | 80 |
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.
Given the following data:
(i) r12.3 (ii) r13.2(iii) r 23.1 (iv) R1.23
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 numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y+2), (Y-3) and (Y+6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.