Part One: 100 Random Telephone Numbers



Part One: 100 Random Telephone Numbers

1. Frequency and Relative Frequency Distribution:

|Last Digit |Frequency |Relative Frequency |

|0 |18 |.18 |

|1 |12 |.12 |

|2 |8 |.08 |

|3 |7 |.07 |

|4 |9 |.09 |

|5 |9 |.09 |

|6 |8 |.08 |

|7 |8 |.08 |

|8 |13 |.13 |

|9 |8 |.08 |

2. Pie Chart

3. Histogram of Frequency Distribution

[pic]

4. Histogram of Relative Frequency Distribution

[pic]

5. The shape of the frequency distribution is skewed to the right because the peak of the data occurs at zero and the other frequencies tail off to the right. Besides the fact that zero and eight happened to be located in the last digits most frequently, there is no real pattern for us to be able to say that the last digit is usually a smaller number or a larger number. Besides a few digits (zero, one, and eight) they are all around the same frequency.

6. The mode of the data is the digit Zero with a frequency of 18.

Part Two: Exercise 12 on page 80

a & b: Frequency and Relative Frequency Distribution (class width of 1000)

|Average State Income |Frequency |Relative Frequency |

|18,001-19,000 |2 |.039 |

|19,001-20,000 |5 |.098 |

|20,001-21,000 |6 |.118 |

|21,001-22,000 |2 |.039 |

|22,001-23,000 |11 |.216 |

|23,001-24,000 |5 |.098 |

|24,001-25,000 |4 |.078 |

|25,001-26,000 |4 |.078 |

|26,001-27,000 |7 |.137 |

|27,001-28,000 |0 |0 |

|28,001-29,000 |1 |.02 |

|29,001-30,000 |1 |.02 |

|30,001-31,000 |1 |.02 |

|31,001-32,000 |2 |.039 |

[pic]

c. Frequency Histogram—It is bell-shaped because the highest frequency is at 22,001-23,000 and it tails off to either side.

[pic]

d. Relative Frequency Histogram

a & b: Frequency and Relative Frequency Distribution (class width of 2000)

|Average State Income |Frequency |Relative Frequency |

|18,000-20,000 |7 |.137 |

|20,001-22,000 |8 |.157 |

|22,001-24,000 |16 |.314 |

|24,001-26,000 |8 |.157 |

|26,001-28,000 |7 |.137 |

|28,001-30,000 |2 |.039 |

|30,001-32,000 |3 |.059 |

[pic]

c. Frequency Histogram—It is bell-shaped because the highest frequency is at 22,001-24,000 and it tails off to either side.

[pic]

d. Relative Frequency Histogram

e. I think that the class width of 1000 provides a better summary, because it is more specific. You are able to see that there is not an average income between $27,001 and $28,000; whereas, with the class width of 2000, the amounts get lumped together with amounts between $26,001 and $27,000, so you are unable to see this information.

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