**Construct histogram of variable width for the following data:**

**a)**

CI |
25-29 |
30-35 |
36-40 |
41-50 |
51-56 |
57-60 |

f |
10 |
24 |
15 |
20 |
12 |
16 |

Solution:

CI | 24.5-29 | 29.5-35.5 | 35.5 – 40.5 | 40.5-50.5 | 50.5-56.5 | 56.5-60.5 |

f | 10 | 24 | 15 | 20 | 12 | 16 |

class width | 5 | 6 | 5 | 10 | 6 | 4 |

length of the rectangles | 10 | 20 | 15 | 10 | 10 | 20 |

**(b)**

CI |
0 – 10 |
10- 15 |
15 – 20 |
20 – 30 |
30 – 40 |
40 – 60 |
60-70 |

f |
20 |
15 |
10 |
25 |
5 |
30 |
50 |

Solution:

CI | 0 – 10 | 10- 15 | 15 – 20 | 20 – 30 | 30 – 40 | 40 – 60 | 60-70 |

f | 20 | 15 | 10 | 25 | 5 | 30 | 50 |

class width | 10 | 5 | 5 | 10 | 10 | 20 | 10 |

Length of the rectangles | 10 | 15 | 10 | 12.5 | 2.5 | 7.5 | 25 |

**Draw given (cumulative frequency curve) for the data given below:**

Class interval |
frequency |

1000 – 1100 |
52 |

1100 – 1200 |
35 |

1200 – 1300 |
25 |

1300 – 1400 |
14 |

1400 – 1500 |
41 |

1500 – 1600 |
33 |

Solution:

Class interval | frequency | Cumulative frequency |

1000 – 1100 | 52 | 52 |

1100 – 1200 | 35 | 87 |

1200 – 1300 | 25 | 112 |

1300 – 1400 | 14 | 126 |

1400 – 1500 | 41 | 167 |

1500 – 1600 | 33 | 200 |

**(b)**

Class interval |
Frequency |

5 – 14 |
4 |

15 – 24 |
8 |

25 – 34 |
12 |

35 – 44 |
14 |

45 – 54 |
6 |

55 – 64 |
4 |

65 – 74 |
18 |

75 – 84 |
24 |

Solution:

Class interval | corrective factor | Frequency | cumulative frequency |

5 – 14 | 4.5 – 14.5 | 4 | 4 |

15 – 24 | 14.5 – 24.5 | 8 | 12 |

25 – 34 | 24.5 – 34.5 | 12 | 24 |

35 – 44 | 34.5 – 44.5 | 14 | 38 |

45 – 54 | 44.5 – 54.5 | 6 | 44 |

55 – 64 | 54.5 – 64.5 | 4 | 48 |

65 – 74 | 64.5 – 74.5 | 18 | 66 |

75 – 84 | 74.5 – 84.5 | 24 | 90 |

**Construct frequency polygon for the following data :**

**a)**

CI |
5 – 10 |
10 – 15 |
15 – 20 |
20 – 25 |
25 – 30 |
30 – 35 |
35 – 40 |
40 – 45 |

f |
2 |
5 |
7 |
6 |
1 |
9 |
14 |
8 |

Solution:

**(b)**

CI |
30-35 |
35-40 |
40-45 |
45-50 |
50-55 |

f |
12 |
20 |
16 |
8 |
14 |

Solution:

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