#### Question

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

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 |

#### Solution

The cumulative frequencies with their respective class intervals are as follows

Weight (in kg) |
Frequency (fi) |
Cumulative frequency |

40 − 45 | 2 | 2 |

45 − 50 | 3 | 2 + 3 = 5 |

50 − 55 | 8 | 5 + 8 = 13 |

55 − 60 | 6 | 13 + 6 = 19 |

60 − 65 | 6 | 19 + 6 = 25 |

65 − 70 | 3 | 25 + 3 = 28 |

70 − 75 | 2 | 28 + 2 = 30 |

Total (n) |
30 |

Cumulative frequency just greater than n/2 (i.e 30/2 = 15) is 19, belonging to class interval 55 − 60.

Median class = 55 − 60

Lower limit (*l*) of median class = 55

Frequency (*f*) of median class = 6

Cumulative frequency (*cf*) of median class = 13

Class size (*h*) = 5

`"Median" = l +((n/2-cf)/f)xxh`

= 55+((15-13)/6)xx5

=55+10/6

= 56.67

Therefore median weight is 56.67 kg

Is there an error in this question or solution?

Solution The distribution below gives the weights of 30 students of a class. Find the median weight of the students. Concept: Median of Grouped Data.