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 |
(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 will use the formula for the regression line in statistics: \[ Y - \bar{Y} = r \times \frac{\sigma_Y}{\sigma_X} \times (X - \bar{X}) \] \[ X - \bar{X} = r \times \frac{\sigma_X}{\sigma_Y} \times (Y - \bar{Y}) \] where: - ______ ___ _______ __________ _________ ________ __________ ________ _________ ________ __________.
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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.
Given the following data:
(i) r12.3 (ii) r13.2(iii) r 23.1 (iv) R1.23
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.
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.
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 |
Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
and