if the mean of the following frequency distribution is 91, find the missing frequency x and y :

classes frequency

0 - 30 12

30-60 21

60 - 90 x

90 -120 52

120 - 150 y

150 - 180 11

total 150

class | frequency (fi) | mid-point (xi) | xi × fi |

0-30 | 12 | 15 | 180 |

30-60 | 21 | 45 | 945 |

60-90 | x | 75 | 75x |

90-120 | 52 | 105 | 5460 |

120-150 | y | 135 | 135y |

150-180 | 11 | 165 | 1815 |

Total 150

mean = ∑(xi × fi)/150 = 91

⇒8400+75x+135y = 13650

⇒5x+9y = 350

Also, 96+x+y = 150

⇒ x+y = 54

solving both equations we get x = 34 and y =20

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