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Sum

Following data gives height in cm (X) and weight in kgs (Y) of 20 boys. Prepare a bivariate frequency table taking class intervals 150-154, 155-159 ...etc. for X and 35-39, 40-44 ...etc. for Y. Also find Marginal frequency distributions.

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#### Solution

Let X: height in cms.

Y: weight in kgs.

Y/X |
150 – 154 | 155 – 159 | 160 – 164 | 165 – 169 |

35 – 39 | III | I | – | – |

40 – 44 | II | III | – | – |

45 – 49 | I | II | I | – |

50 – 54 | I | I | III | II |

Bivariate frequency distribution is

Y/X |
150 – 154 | 155 – 159 | 160 – 164 | 165 – 169 | Total (f_{y}) |

35 – 39 | 3 | 1 | – | – | 4 |

40 – 44 | 2 | 3 | – | – | 5 |

45 – 49 | 1 | 2 | 1 | – | 4 |

50 – 54 | 1 | 1 | 3 | 2 | 7 |

Total (f_{x}) |
7 | 7 | 4 | 2 | 20 |

Marginal distribution for X (height in cms)

X |
150 – 154 | 155 – 159 | 160 – 164 | 165 – 169 | Total |

Frequency |
7 | 7 | 4 | 2 | 20 |

Marginal distribution for Y (weight in kgs)

Y |
35 – 39 | 40 – 44 | 45 – 49 | 50 – 54 | Total |

Frequency |
4 | 5 | 4 | 7 | 20 |

Concept: Classification and Tabulation of Bivariate Data - Marginal Frequency Distributions

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