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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Given the following data: ,
and
then find (i) r12.3 (ii) r13.2 (iii) r23.1 (iv) R1.23
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
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 the given data, two frequencies are missing and its mean is found to be 1.46.
| No. of Accidents (x) | Frequencies (f) |
|---|---|
| 0 | 46 |
| 1 | ? |
| 2 | ? |
| 3 | 25 |
| 4 | 10 |
| 5 | 5 |
| Total | 200 |
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 |
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.
The following is the distribution of age (in years) of 800 workers:
| Age Group | No. of Workers |
|---|---|
| 20 — 25 | 50 |
| 25 — 30 | 70 |
| 30 — 35 | 100 |
| 35 — 40 | 180 |
| 40 — 45 | 150 |
| 45 — 50 | 120 |
| 50 — 55 | 70 |
| 55 — 60 | 60 |