Probability and Statistics

1. Construct a stem-and-leaf plot for the grades of 100 graduating students in their comprehensive examination.

GRADES OF 100 GRADUATING STUDENTS |

84 | 86 | 85 | 87 | 77 | 89 | 83 | 80 | 79 | 97 |

84 | 76 | 76 | 88 | 75 | 84 | 92 | 86 | 93 | 83 |

89 | 86 | 78 | 87 | 83 | 83 | 74 | 79 | 81 | 81 |

70 | 84 | 89 | 85 | 83 | 91 | 91 | 80 | 90 | 85 |

90 | 76 | 91 | 84 | 76 | 69 | 75 | 95 | 74 | 84 |

79 | 81 | 86 | 71 | 91 | 69 | 91 | 89 | 95 | 81 |

91 | 82 | 85 | 76 | 80 | 91 | 82 | 81 | 85 | 88 |

82 | 67 | 91 | 80 | 74 | 81 | 72 | 89 | 88 | 83 |

77 | 76 | 81 | 80 | 82 | 79 | 93 | 86 | 87 | 80 |

74 | 83 | 81 | 83 | 83 | 81 | 93 | 80 | 75 | 70 |

STEM | LEAVES |

6 | 7, 9, 9 | | | |

7 | 0, 0,1,2,4, 4, 4, 4, 5, 5, 5,6,6,6,6,6,6,7,7,8,9,9,9,9 | |

8 | 0,0,0,0,0,0,0, 1, 1, 1, 1, 1,1,1,1,1,2, 2, 2,2,3, 3, 3, 3, 3, 3, 3, 3,3, 4, 4, 4, 4, 4, 4, 5, 5, 5,5,5, 6, 6, 6,6,6, 7, 7,7, 8, 8, 8, 9, 9, 9,9,9 |

9 | 0,0,1,1,1,1,1,1,1,1,2,3,3,3,5,5,7 | | | |

2. Consider the problem in number 1, construct a frequency distribution table which includes class intervals, class frequency, class mark and the less than and greater than cumulative frequency.

Class Interval | f | M | <cumf | >cumf |

67-72 | 7 | 69.5 | 7 | 100 |

73-78 | 16 | 75.5 | 23 | 93 |

79-84 | 39 | 81.5 | 62 | 77 |

85-90 | 23 | 87.5 | 85 | 38 |

91-96 | 14 | 93.5 | 99 | 15 |

97-102 | 1 | 99.5 | 100 | 1 |

  | 100 |   |   |   |

3. Consider the problem in number 1, construct a histogram and frequency polygon.

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