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
(i) the expected advertising expenditure of the company if sale is Rs. 125 lakhs, and
(ii) the expected sales of the company if the advertising expenditure is Rs 32 lakhs.
We are given: [ \bar{X} = 20, \quad \bar{Y} = 100, \quad \sigma_X = 3, \quad \sigma_Y = 12, \quad r = 0.8 ] We will use the formulas for regression lines: 1. Regression of (X) on (Y): [ X _________ _________ ___ _______ ________ _________ ___ ______ __________ ___.
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Calculate Karl Pearson's coefficient of correlation between X and Y for the following data: and
.
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 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.
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.
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.
(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.
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 |