Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
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.
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.
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 |
If two new variables X' and Y' are obtained by adding 50 to each value of X and 100 to each value of Y, respectively, calculate the correlation coefficient between X' and Y' using the above data. Also compare the results.
If (A) = 90, (AB) = 40, N = 150 and (β) = 80 then (αβ) = 30.
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%.
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 |
Find the missing frequencies.
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.