Find the median of the following data set which gives the marks out of 50 of 150 students in annual examination.

Marks obtained | Number of Families |
---|---|

20 | 6 |

29 | 9 |

31 | 32 |

33 | 15 |

42 | 15 |

19 | 12 |

35 | 19 |

43 | 17 |

39 | 20 |

25 | 17 |

Mathematics

Class 8

138

Knowledge

Knowledge

Answer / Solution

Answer / Solution

To find the median marks of 150 students in annual examination, first arrange the marks in ascending order, then the frequency tables as follows:

Marks Obtained | Number of Students (f_{i}) |
Cumulative Frequency |
---|---|---|

19 | 12 | 12 |

20 | 6 | 12 + 6 = 18 |

25 | 17 | 18 + 17 = 35 |

29 | 9 | 35 + 9 = 44 |

31 | 22 | 44 + 22 = 66 |

33 | 13 | 66 + 13 = 79 |

35 | 19 | 79 + 19 = 98 |

39 | 20 | 98 + 20 = 118 |

42 | 15 | 118 + 15 = 133 |

43 | 17 | 133 + 17 = 150 |

∑f = 150 |

Here, Total Number of Students are 150 which is an even value. Therefore, the median will be the average of the (n/2)^{th} observation i.e.

(n/2)^{th} observation is = 150/2 i.e. 75th.

In the cumulative frequency table above, 75th locating in 79 i.e. whose cumulative frequency is greater than or nearest to (n/2)^{th} term.

Thus the corresponding value of x in is a median value.

Marks Obtained | Number of Students (f_{i}) |
Cumulative Frequency |
---|---|---|

33 | 13 | 79 |

So, the median value is 33.

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