Question

Age | Number |

16-20 | 5 |

21-25 | 6 |

26-30 | 12 |

31-35 | 14 |

36-40 | 26 |

41-45 | 12 |

46-50 | 16 |

51-55 | 9 |

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Updated on : 2022-09-05

Solution

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Class | $f_{i}$ | Cumulative frequency | $x_{i}$ | $∣x_{i}−M∣$ | $f_{i}∣x_{i}−M∣$ |

15.5-20.5 | 5 | 5 | 18 | 20 | 100 |

20.5-25.5 | 6 | 11 | 23 | 15 | 90 |

25.5-30.5 | 12 | 23 | 28 | 10 | 120 |

30.5-35.5 | 14 | 37 | 33 | 5 | 70 |

35.5-40.5 | 26 | 63 | 38 | 0 | 0 |

40.5-45.5 | 12 | 75 | 43 | 5 | 60 |

45.5-50.5 | 16 | 91 | 48 | 10 | 160 |

50.5-55.5 | 9 | 100 | 53 | 15 | 135 |

Total | 100 | 735 |

$2N =2100 =50$

which occurs in the cumulative frequency $63$.

Hence, the median class is $35.5−40.5$.

Median $M=l+f_{m}2N −C_{f_{−1}} ×h$

$=35.5+2650−37 ×5$

$=35.5+2613 ×5$

$⇒M=35.5+2.5=38$

Mean deviation about the median is

$M.D.(M)=N1 i=1∑8 f_{i}∣x_{i}−M∣$

$=1001 ×735=7.35$

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