Find the missing frequencies f1 and f2 in the following frequency distribution, if it is known that the mean of the distribution is 1.46

1 | 0 | 1 | 2 | 3 | 4 | 5 | Total |
---|---|---|---|---|---|---|---|

f1 | 46 | f1 | f2 | 25 | 10 | 5 | 200 |

Find the missing frequencies f1 and f2 in the following frequency distribution, if it is known that the mean of the distribution is 1.46

1 | 0 | 1 | 2 | 3 | 4 | 5 | Total |
---|---|---|---|---|---|---|---|

f1 | 46 | f1 | f2 | 25 | 10 | 5 | 200 |

xi | fi | fixi |
---|---|---|

0 | 46 | 0 |

1 | f1 | f1 |

2 | f2 | 2f2 |

3 | 25 | 75 |

4 | 10 | 40 |

5 | 5 | 25 |

N = 86 + f_{1} + f_{2}

We have N = 200

∴ 200 = 86 + f_{1} + f_{2}

Thus, f_{1} = 114 - f_{2} …(i)

Mean = 1.46

292 = 140 + f_{1} + 2f_{2}

⇒ f_{1} + 2f_{2} = 152 …(ii)

Solving (i) and (ii), we get

114 - f_{2} + 2f_{2} = 152

Thus, f_{2} = 38

Hence, f_{1} = 114 - 38 = 76