Find the difference between the upper limit of the median class and the lower limit of the modal class in the data given below.

class 65 - 85 85-105 105 - 125 125 - 145 145 - 165 165 - 185

frequency 4 5 13 20 14 12

Firstly, we make the cumulative table :

Class | Frequency | Cumulative Frequency |

65-85 | 4 | 4 |

85-105 | 5 | 9 |

105-125 | 13 | 22 |

125-145 | 20 | 42 |

145-165 | 14 | 56 |

165-185 | 12 | 68 |

We have N= 68, thus, N/2 = 34

The cumulative frequency just greater than 34 is 42 and the corresponding class is 125-145.

Thus, upper limit of median class is 145

And,

maximum frequency is 20 and the corresponding class is 125-145. So, 125-145 is the modal class.

Thus, lower limit of modal class = 125

So,

Difference between upper limit of median class and lower limit of modal class = 145-125= 20

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