Describe the conditions for consistency of the data. In a sample of 1000 students admitted
in a college, 500 belonged to rural areas and the rest belonged to urban areas. The number
of students belonging CBSE Board from both areas are 200 and 100, respectively.
Calculate the coefficient of association between area and the Board of Education.
To calculate the coefficient of association between the area (rural or urban) and the Board of Education (CBSE or other), we can use a measure of association such as the Phi coefficient (φ) for a 2x2 contingency table. The Phi coefficient is a measure of the strength and direction of association between two categorical variables.
In your case, the data can be represented in the following 2x2 contingency table:
```
Rural Urban
CBSE Board 200 100
Other Board 300
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Calculate the rank correlation coefficient for the following data:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Mathematics | 76 | 80 | 85 | 80 | 78 | 65 | 85 | 80 |
| Physics | 91 | 78 | 82 | 78 | 86 | 80 | 88 | 92 |
For the following distribution, calculate first four central moments using recurrence
relations. Also find the coefficients of skewness and kurtosis.
| Marks: | 2.7- 7.5 | 7.5- 12.5 | 12.5- 17.5 | 17.5- 22.5 | 22.5- 27.5 | 27.5- 32.5 | 32.5- 37.5 |
| Frequency: | 06 | 13 | 23 | 39 | 19 | 15 | 05 |
Calculate the first, second and third quartile for following data:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 05 | 15 | 30 | 12 | 08 |
Derive the formula for the coefficient of partial correlation coefficient R1.23, R2.13 and R3.12 for the following data:
| X1 | 10 | 20 | 30 | 40 | 50 |
| X2 | 20 | 30 | 40 | 50 | 60 |
| X3 | 30 | 40 | 50 | 60 | 70 |
If the regression coefficients 
of a data are 1.6 and 0.4, respectively, then the value of r(X, Y) is 0.8.