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Question
The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class.
Also prepare marginal distributions :
(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )
Solution
We can tublate the bi- variate frequency
distribution in a table shown below :
| x → | 2 | 3 | 4 | 5 | Total |
| y↓ | |||||
| 6 | - | - | | | (2) | | | | (3) | 5 |
| 7 | | (1) | - | | | (2) | | | (2) | 5 |
| 8 | | | (2) | | | (3) | | | (2) | - | 7 |
| 9 | | (1) | - | | | (2) | ≠ | 3 |
| Total | 4 | 3 | 8 | 5 | 20 |
Marginal distribution of X :
| X | 2 | 3 | 4 | 5 | Total |
| Frequency | 4 | 3 | 8 | 5 | 20 |
Marginal distribution of y :
| Y | 6 | 7 | 8 | 9 | Total |
| Frequency | 5 | 5 | 7 | 3 | 20 |
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