If the median of the distribution is given below is 28.5, find the values of x and y

Class interval | Frequency |

0 - 10 | 5 |

10 - 20 | x |

20 - 30 | 20 |

30 - 40 | 15 |

40 - 50 | y |

50 - 60 | 5 |

Total | 60 |

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#### Solution

The cumulative frequency for the given data is calculated as follows

Class interval | Frequency | Cumulative frequency |

0 - 10 | 5 | 5 |

10 - 20 | x | 5+ x |

20 - 30 | 20 | 25 + x |

30 - 40 | 15 | 40 + x |

40 - 50 | y | 40+ x + y |

50 - 60 | 5 | 45 + x + y |

Total (n) | 60 |

From the table, it can be observed that n = 60

45 + x + y = 60

x + y = 15 (1)

Median of the data is given as 28.5 which lies in interval 20 - 30.

Therefore, median class = 20 - 30

Lower limit (l) of median class = 20

Cumulative frequency (cf) of class preceding the median class = 5 + x

Frequency (f) of median class = 20

Class size (h) = 10

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

28.5 = 20 + [(60/2-(5+x))/20]xx10

8.5 = ((25-x)/2)

17 = 25 - x

8 + y = 15

y = 7

Hence, the values of x and y are 8 and 7 respectively.

Concept: Median of Grouped Data

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