Sum
Construct a bivariate frequency distribution table of the marks obtained by students in English (X) and Statistics (Y).
Marks in Statistics (X) |
37 | 20 | 46 | 28 | 35 | 26 | 41 | 48 | 32 | 23 | 20 | 39 | 47 | 33 | 27 | 26 |
Marks in English (Y) |
30 | 32 | 41 | 33 | 29 | 43 | 30 | 21 | 44 | 38 | 47 | 24 | 32 | 21 | 20 | 21 |
Construct a bivariate frequency distribution table for the above data by taking class intervals 20 – 30, 30 – 40, ...... etc. for both X and Y. Also find the marginal distributions and conditional frequency distribution of Y when X lies between 30 – 40.
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Solution
Let X: Marks in Statistics
Y: Marks in English
Bivariate frequency table can be prepared by taking class intervals 20 – 30, 30 – 40,…, etc for both X and Y. Bivariate frequency distribution is as follows:
Y/X | 20 – 30 | 30 – 40 | 40 –50 | Total (f_{y}) |
20 – 30 | II | II | I | 5 |
30 – 40 | III | II | II | 7 |
40 – 50 | II | I | I | 4 |
Total (f_{x}) | 7 | 5 | 4 | 16 |
Marginal frequency distribution of X:
X | 20 – 30 | 30 – 40 | 40 – 50 | Total |
Frequency | 7 | 5 | 4 | 16 |
Marginal frequency distribution of Y:
Y | 20 – 30 | 30 – 40 | 40 – 50 | Total |
Frequency | 5 | 7 | 4 | 16 |
Conditional frequency distribution of Y when X lies between 30 – 40:
Y | 20 – 30 | 30 – 40 | 40 –50 | Total |
Frequency |
2 | 2 | 1 | 5 |
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