#### Question

The table below shows the salaries of 280 persons :

Salary (In thousand Rs) |
No. of Persons |

5 – 10 | 49 |

10 – 15 | 133 |

15 – 20 | 63 |

20 – 25 | 15 |

25 – 30 | 6 |

30 – 35 | 7 |

35 – 40 | 4 |

40 – 45 | 2 |

45 – 50 | 1 |

Calculate the median salary of the data.

#### Solution

Salary (In thousand Rs) |
Frequency |
CF |

5 – 10 | 49 | 49 |

10 – 15 | 133 | 182 |

15 – 20 | 63 | 245 |

20 – 25 | 15 | 260 |

25 – 30 | 6 | 266 |

30 – 35 | 7 | 273 |

35 – 40 | 4 | 277 |

40 – 45 | 2 | 279 |

45 – 50 | 1 | 280 |

`N/2 = 280/2 = 140`

The cumulative frequency which is greater than and nearest to 140 is 182.

Median class = 10-15

We also have,

*l* (lower limit of median class) = 10

*h* (class size) = 5

*n* (number of observations) = 280

*cf* = (cumulative frequency of the class preceding the median class) = 49

*f* (frequency of median class) = 133

Median for grouped data is given by the formula :

Median = `l + ((n/2 - cf)/f) xx h`

where *f *is the frequency of median class and cf is the cumulative frequency of previous class.

Median = `10 + (140 - 49)/133 xx 5 = 13.42`

Is there an error in this question or solution?

Solution The Table Below Shows the Salaries of 280 Persons : Calculate the Median Salary of the Data. Concept: Median of Grouped Data.