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Length(in mm) |
Number of leaves |

118-126 |
3 |

127-135 |
5 |

136-144 |
9 |

145-153 |
12 |

154-162 |
5 |

163-171 |
4 |

172-180 |
2 |

Answer :

Since the data are not continuous reduce 0.5 in the lower limit and add 0.5 in the upper limit.

Class Interval | Frequency | Cumulative frequency |

117.5-126.5 | 3 | 3 |

126.5-135.5 | 5 | 8 |

135.5-144.5 | 9 | 17 |

144.5-153.5 | 12 | 29 |

153.5-162.5 | 5 | 34 |

162.5-171.5 | 4 | 38 |

171.5-180.5 | 2 | 40 |

So, n = 40 and \( \frac{n}{2} \ = \ 20 \)

Median class = 144.5 -153.5

then, \( l = 144.5, cf = 17, f = 12, h = 9 \)

Now we know that, Median \(= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h \)

\(\Rightarrow \) Median \( = \ 144.5 \ + \ ( \frac{20 \ - \ 17}{12}) \ × \ 9 \)

\( = \ 144.5 \ + \ \frac{3}{12} \ × \ 9 \)

\( = \ 144.5 \ + \ 2.25 \ = \ 146.75 \)

\(\therefore \) The median length of the leaves = 146.75 mm.

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