State whether the following statements are true or false and also give the reason in support of your answer:
(a) If and
are the variate values of two variables X and Y, and their geometric means are G1 and G2, respectively, then geometric mean of
will be (G1/G2).
(b) If X and Y are two independent variables and the variables and
, 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 b.
(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 and
then
.
(a) False – The geometric mean of the ratio of two variables is not equal to the ratio of their geometric means. The correct relationship is that the geometric mean of (X/Y) is the geometric mean of ______ ______ __________ ____ ___ _____.
_________ _____ __________ _______ _________ ___ _________ _____.
________ _____ ___ _____ ______ ______.
____ ______ ________ ___ ____ __________ _____ _______ __________ ___.
________ __________ _________ __________ _________ __________.
____ ______ __________ _________ __________ ______ ______ _______ ___ ______ ________ __________.
________ ______ _______ _______ _______ ____.
_________ ___ ______ _____ ________ __________.
_____ __________ _______ ___ _____ _______ ____ ________ ________ _________ _________.
___ ________ __________ ___ ________ ___ _____ ____ __________ ____ ________.
_________ ________ ___ ___ ____ _______ _____.
______ __________ ________ _______ _______ _____ ______ ___ ___ __________ ______ _____.
__________ ___ _______ _______ ______ ________ _________ ________.
_____ __________ __________ _______ _________ ________ ____.
_______ _______ ___ ___ __________ _________ ________ ___ ________ ______ _________ ______.
_____ ___ _______ ____ _____ ______ _____.
____ _________ _________ __________ _________ _______ ________ ___ ___.
___ ____ _______ _______ ____ __________ __________ __________ ______.
___ _________ ____ ________ ____ _______ ________ _____ ________.
_________ _______ ____ _______ ______ _________ __________ _______ __________ __________.
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________ _____ _______ _______ ______ ______ ________ _______ _________.
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Calculate Karl Pearson's coefficient of correlation between X and Y for the following data: and
.
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.
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.
The following table shows the information as:
| Statistical Measures | Advertisement Expenditure (X) (Rs. Lakhs) | Sales (Y) (Rs Lakhs) |
|---|---|---|
| Mean | 20 | 100 |
| Standard Deviation | 03 | 12 |
. Then find
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.
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.
(a) In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as and
. The standard deviation of
, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y.