Prepare a bivariate frequency distribution for the following data, taking class intervals for X as 35 – 45, 45 – 55, …. etc and for Y as 115 – 130, 130 – 145, … etc. where X denotes the age in years and Y denotes blood pressure for a group of 24 persons.

(55, 151) (36, 140) (72, 160) (38, 124) (65, 148) (46, 130) (58, 152) (50, 149) (38, 115) (42, 145) (41, 163) (47, 161) (69, 159) (60, 161) (58, 131) (57, 136) (43, 141) (52, 164) (59, 161) (44, 128) (35, 118) (62, 142) (67, 157) (70, 162)

Also, find Marginal frequency distribution of X.

#### Solution

Given X = Age in years

Y = Blood pressure

Bivariate frequency table can be prepared by taking class intervals 35 – 45, 45 – 55, …. etc for X and 115 – 130, 130 – 145, … etc for Y.

Bivariate frequency distribution is as follows:

Blood Pressure (y)/Age in years(X) |
35 – 45 |
45 – 55 |
55 – 65 |
65 – 75 |
Total (f_{y}) |

115 – 130 |
IIII (4) | – | – | – | 4 |

130 – 145 |
II (2) | I (1) | III (3) | – | 6 |

145 – 160 |
I (1) | I (1) | II (2) | III 3) | 7 |

160 – 175 |
I (1) | II (2) | II (2) | II (2) | 7 |

Total (f_{x}) |
8 | 4 | 7 | 5 | 24 |

Marginal frequency distribution of X:

X |
35 – 45 | 45 – 55 | 55 – 65 | 65 – 75 | Total |

Frequency |
8 | 4 | 7 | 5 | 24 |