#### Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |

No. of persons | 5 | 25 | ? | 18 | 7 |

#### Solution

Class interval | Frequency | Cumulative frequency |

0 - 10 | 5 | 5 |

10 - 20 | 25 | 30 |

20 - 30 | x | 30 + x |

30 - 40 | 18 | 48 + x |

40 - 50 | 7 | 55 + x |

N = 55 + x |

Given

Median = 24

Then median class = 20 - 30

l = 20, h = 30 - 20 = 10, F = 30 and f = x

Median `=l+{(N/2-F)/f}xxh`

`24=20+((55+x)/2-30)/x xx10`

`24 - 20=((55+x)/2-30)/x xx10`

`4x=((55+x)/2-30)xx10`

`4x xx2=(55 + x -60)xx10`

8x = 550 + 10x - 600

10x - 8x = 600 - 550

2x = 50

x = 25

∴ Missing frequency = 25

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#### APPEARS IN

Solution Calculate the Missing Frequency from the Following Distribution, It Being Given that the Median of the Distribution is 24. Concept: Median of Grouped Data.