The following frequency distribution table shows the distances travelled by some rickshaws in a day. Observe the table and answer the following questions

Class (daily distance travelled in km) | continuous classes | Frequency (no.of. rickshaws) | Cumulative frequency less than type |

60 - 64 | 59.5 - 64.5 | 10 | 10 |

65 - 69 | 64.5 -69.5 | 34 | 10+34=44 |

70 - 74 | 69.5 - 74.5 | 58 | 44+58=102 |

75 - 79 | 74.5 - 79.5 | 82 | 102+82=184 |

80 - 84 | 79.5 - 84.5 | 10 | 184+10=194 |

85 - 89 | 84.5 - 89.5 | 6 | 194+6=200 |

1) Which is the modal class? Why?

2) Which is the median class and why?

3) Write the cumulative frequency (C.F) of the class preceding the median class.

4) What is the class interval (h) to calculate median?

#### Solution

1) Model class is class that contains highest frequency i.e.

highest frequency = 82

highest frequency class = 75 - 79

2) Median class is the class that contain `("N"/2)^("th")` term. Where N is total frequency.

N = 200

`("N"/2) = 100`

`("N"/2)^"th"` term will lie in (70- 74) class

(iii) Cumulative frequency = 44

(iv) Median class = 70 – 74

OR

69.5 – 74.5 (continuous)

h = U.l. -L.l.

= 74.5 -69.5 = 5