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Weight(in kg) |
40-45 |
45-50 |
50-55 |
55-60 |
60-65 |
65-70 |
70-75 |

Number of students |
2 |
3 |
8 |
6 |
6 |
3 |
2 |

Answer :

Class Interval |
Frequency |
Cumulative frequency |

40-45 | 2 | 2 |

45-50 | 3 | 5 |

50-55 | 8 | 13 |

55-60 | 6 | 19 |

60-65 | 6 | 25 |

65-70 | 3 | 28 |

70-75 | 2 | 30 |

We have n = 30 \( \Rightarrow \ \frac{n}{2} \ = \ 15 \)

The cumulative frequency just greater than \( \frac{n}{2} \) is 19 and the corresponding class is 55 - 60.

Thus, 55 - 60 is the median class such that :

\( \frac{n}{2} = 15 , l = 55 , f = 6 , cf = 13 \ and \ h = 5 \)

Median \(= \ l \ + \ ( \frac{ \frac{n}{2} \ - \ cf}{f} ) \ × \ h \)

\(= \ 55 \ + \ ( \frac{15 \ - \ 13}{6}) \ × \ 5 \)

\(= \ 55 \ + \ \frac{2}{6} \ × \ 5 \ = \)

\( 55 \ + \ 1.67 \ = \ 56.67 \)

\(\therefore \) The median weight = 56.67 kg .

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