#### Question

The content of 100 match boxes were checked to detemine the number of matches they contained .

no of matches |
35 | 36 | 37 | 38 | 39 | 40 | 41 |

no of boxes |
6 | 10 | 18 | 25 | 21 | 12 | 8 |

(1) Calculate, correct to one decimal place, the means number of matches per box .

(2) Determine how many extra matches would have to be added to the the total contents of the total content of the 100 boxes to bring the mean up to exactly 39 matches.

#### Solution

No of matches (x) |
No.of boxes (F) |
fx |

35 | 6 | 210 |

36 | 10 | 360 |

37 | 18 | 666 |

38 | 25 | 950 |

39 | 21 | 819 |

40 | 12 | 480 |

41 | 8 | 328 |

Total | 100 | 3813 |

(1)`barx=(∑ fx )/(∑f)=3813/100=38.13`

(2) In the second case ,

New mean = 39 matches

Total contents =39 x 100 = 3900

But total number of matches already give = 3813

Number of new matches to be added = 3900 - 3813 = 87

Is there an error in this question or solution?

Solution The Content of 100 Match Boxes Were Checked to Detemine the Number of Matches They Contained . Concept: Measures of Central Tendency - Mean, Median, Mode for Raw and Arrayed Data.