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Question
Following data gives the age of husbands (X) and age of wives (Y) in years. Construct a bivariate frequency distribution table and find the marginal distributions.
| X | 27 | 25 | 28 | 26 | 29 | 27 | 28 | 26 | 25 | 25 | 27 |
| Y | 21 | 20 | 20 | 21 | 23 | 22 | 20 | 20 | 19 | 19 | 23 |
| X | 26 | 29 | 25 | 27 | 26 | 25 | 28 | 25 | 27 | 26 | |
| Y | 19 | 23 | 23 | 22 | 21 | 20 | 22 | 23 | 22 | 21 |
Find conditional frequency distribution of age of husbands when the age of wife is 23 years.
Solution 1
Let X: Age of husbands in years
Y: Age of Wives in years
| Y/X | 25 | 26 | 27 | 28 | 29 |
| 1 | II | I | – | – | – |
| 2 | II | I | – | II | – |
| 3 | – | III | I | – | – |
| 4 | – | – | III | I | – |
| 5 | II | – | I | – | II |
Bivariate frequency distribution is
| Y/X | 2 | 3 | 4 | 5 | 6 | Total () |
| 1 | – | 1 | 2 | – | 1 | 4 |
| 2 | – | 1 | – | 2 | – | 3 |
| 3 | 2 | 1 | 3 | – | – | 6 |
| 4 | – | 2 | – | – | 1 | 3 |
| 5 | 5 | – | 3 | 1 | – | 9 |
| Total () | 7 | 5 | 8 | 3 | 2 | 26 |
Marginal frequency distribution of X (Age of husbands)
| X | 25 | 26 | 27 | 28 | 29 | Total |
| () | 6 | 5 | 5 | 3 | 2 | 21 |
Margin frequency distribution of Y (Age of wives)
| Y | 19 | 20 | 21 | 22 | 23 | Total |
| () | 3 | 5 | 4 | 4 | 5 | 21 |
Conditional distribution of Xage of husbands) when Y (age of wives) is 23 years.
| X | 25 | 26 | 27 | 28 | 29 | Total |
| Frequency | 2 | – | 1 | – | 2 | 5 |
Solution 2
Given, X = Age of Husbands (in years)
Y = Age of Wives (in years)
Now, minimum value of X is 25 and maximum value is 29.
Also, minimum value of Y is 19 and maximum value is 23.
Bivariate frequency distribution is as follows:
| Y/X | 25 | 26 | 27 | 28 | 29 | Total (fy) |
| 19 | II | I | – | – | – | 3 |
| 20 | II | I | – | II | – | 5 |
| 21 | – | III | I | – | – | 4 |
| 22 | – | – | III | I | – | 4 |
| 23 | II | – | I | – | II | 5 |
| Total (fx) | 6 | 5 | 5 | 3 | 2 | 21 |
Marginal frequency distribution of X:
| X | 25 | 26 | 27 | 28 | 29 | Total |
| Frequency | 6 | 5 | 5 | 3 | 2 | 21 |
Marginal frequency distribution of Y:
| Y | 19 | 20 | 21 | 22 | 23 | Total |
| Frequency | 3 | 5 | 4 | 4 | 5 | 21 |
Conditional frequency distribution of X when Y is 23:
| X | 25 | 26 | 27 | 28 | 29 | Total |
| Frequency | 2 | 0 | 1 | 0 | 2 | 5 |
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