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Following tale gives income (X) and expenditure (Y) of 25 families:

Y/X |
200 – 300 |
300 – 400 |
400 – 500 |

200 – 300 |
IIII I | IIII I | I |

300 – 400 |
– | IIII | IIII I |

400 – 500 |
– | – | II |

Find Marginal frequency distributions of income and expenditure.

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#### Solution

The bivariate frequency distribution is

Y/X |
200 – 300 |
300 – 400 |
400 – 500 |
Total (f_{y}) |

200 – 300 |
6 | 6 | 1 | 13 |

300 – 400 |
0 | 4 | 6 | 10 |

400 – 500 |
0 | 0 | 2 | 2 |

Total (f_{x}) |
6 | 10 | 9 | 25 |

The Marginal frequency distributions of income (X):

X |
200 – 300 | 300 – 400 | 400 – 500 | Total |

Frequency |
6 | 10 | 9 | 25 |

The Marginal frequency distributions of expenditure (Y):

Y |
200 – 300 | 300 – 400 | 400 – 500 | Total |

Frequency |
13 | 10 | 2 | 25 |

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