Calculate Karl Pearson's coefficient of correlation between X and Y for the following data:
and
Karl Pearson's coefficient of correlation (\( r \)) is given by the formula: \[ r = \frac{N\sum XY - _______ ________ ____ _____ ______ _______ ________ ________ _________.
_____ ______ _______ ___ _______ __________ ________ ________ ______ ______ ______ ________.
______ _________ _________ ________ _______ _______ __________ __________ _____ ___ _________.
_________ _________ ______ ___ ___ _______ ___ ______ _____ __________ _____ ___.
____ _____ ______ _____ _______ _____ _________ _________.
_____ _______ __________ _______ ______ _________ ___ ___ _____ ________.
_______ _____ __________ ___ _____ ________ ________ ________ _______ _______ ________ __________.
___ ______ ___ __________ ____.
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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 |
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.
Given the following data:
(i) r12.3 (ii) r13.2(iii) r 23.1 (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 |
State whether the following statements are true or false and also give the reason in support of your answer:
(a) if are the variate values of two variables X and and their geometric means are Grand G₂, respectively, then geometric mean of
will be (G1/G2).
(b) If X and Y are two independent variables and the variables U=X+ Y and V= X-Y, 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 byx.
(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
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 |