Problem 9E

Refer to Table 1.4 (in Section 1.3).

a. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the frequencies.

b. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the densities.

c. Compare the histograms in parts (a) and (b) with the histogram in Figure 1.8, for which the heights are the relative frequencies. Are the shapes of the histograms the same?

Solution 9E

Step1 of 3:

We have a data set from section 1.3, Table 1.4.

Class interval(g/gal) |
Frequency |
Relative Frequency |
Density |

1-<3 |
12 |
0.1935 |
0.0968 |

3-<5 |
11 |
0.1774 |
0.0887 |

5-<7 |
18 |
0.2903 |
0.1452 |

7-<9 |
9 |
0.1452 |
0.0726 |

9-<11 |
5 |
0.0806 |
0.0403 |

11-<13 |
1 |
0.0161 |
0.0081 |

13-<15 |
2 |
0.0323 |
0.0161 |

15-<17 |
0 |
0 |
0 |

17-<19 |
2 |
0.0323 |
0.0161 |

19-<21 |
1 |
0.0161 |
0.0081 |

21-<23 |
0 |
0 |
0 |

23-<25 |
1 |
0.0161 |
0.0081 |

We need to find,

a).Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the frequencies.

b).Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the densities.

c).Compare the histograms in parts (a) and (b) with the histogram in Figure 1.8, for which the heights are the relative frequencies. Are the shapes of the histograms the same?

Step2 of 3:

a).

A histogram in which the heights of the rectangles are equal to the frequencies is given below

b).

A histogram in which the heights of the rectangles are equal to the densities is given below

Step3 of 3:

c).

By comparing Histogram graphs in part(a) and part(b) we can say that Yes, the shapes of the histograms are the same.