11. Following is the distribution of marks obtained by 60 students: Calculate the arithmetic mean

MarksMorethan 0more than 10More than20More than 30More than 40More than 50No ofstudents60564020103

More than | Cumulative frequency | Class | frequency(f_{i}) |
f_{i}.x_{i} |

More than 0 | 60 | 0-10 | 4 | 20 |

More than 10 | 56 | 10-20 | 16 | 240 |

More than 20 | 40 | 20-30 | 20 | 500 |

More than 30 | 20 | 30-40 | 10 | 350 |

More than 40 | 10 | 40-50 | 7 | 315 |

More than 50 | 3 | 50-60 | 3 | 165 |

Now using direct method for finding the mean of 60 student,

Mean = $\frac{\sum {f}_{i}{x}_{i}}{\sum {f}_{i}}$ = $\frac{1590}{60}=26.5$

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