Relative Frequencies for Comparisons. In Exercises 15 and 16, construct the relative frequencies and answer the given questions.

Oscar Winners Construct one table (similar to Table 29 on page 50) that includes relative frequencies based on the frequency distributions from Exercises 5 and 6, and then compare the ages of Oscar-winning actresses and actors. Are there notable differences?

Answer :

Step 1 of 1 :

Given, the ages of Oscar-winning actresses and the frequency

Age when Oscar was won |
Frequency |

20-29 |
27 |

30-39 |
34 |

40-49 |
13 |

50-59 |
2 |

60-69 |
4 |

70-79 |
1 |

80-89 |
1 |

We have to find the relative frequency for comparison

The total frequency = 82

Relative frequency =

Example :

Relative frequency =

= 32.92

class width : the difference between the upper and lower class limit.

Example : 29-2

= 9

class midpoints : (lower class limit + upper class limit)/ 2

Example : (20+29)/2

= 24.5

class boundaries :

Upper class boundary = Upper limit + () unit of measurement

Ex: 4.9 is the upper class limit and unit of measurement is 0.1

Therefore ,

Upper class boundary = 29 + () 1

= 4.95

Lower class boundary = Lower limit + () unit of measurement

Ex: 4.9 is the upper class limit and unit of measurement is 0.1

Therefore ,

Upper class boundary = 20 + () 1

= 3.05

Age when Oscar was won |
Frequency |
Relative frequency |
Class width |
Class midpoints |
Class boundaries |

20-29 |
27 |
32.92 |
9 |
24.5 |
(20.5 , 29.5) |

30-39 |
34 |
41.46 |
9 |
34.5 |
(30.5 , 39.5) |

40-49 |
13 |
15.85 |
9 |
44.5 |
(40.5 , 49.5) |

50-59 |
2 |
2.43 |
9 |
54.5 |
(50.5 , 59.5) |

60-69 |
4 |
4.88 |
9 |
64.5 |
(60.5 , 69.5) |

70-79 |
1 |
1.22 |
9 |
74.5 |
(70.5 , 79.5) |