#### Question

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss | No. of tosses |

0 | 38 |

1 | 144 |

2 | 342 |

3 | 287 |

4 | 164 |

5 | 25 |

Total | 1000 |

#### Solution 1

No. of heads per toss | No. of tosses | fx |

0 | 38 | 0 |

1 | 144 | 144 |

2 | 342 | 684 |

3 | 287 | 861 |

4 | 164 | 656 |

5 | 25 | 125 |

N = 1000 | `sum`fx = 2470 |

Mean number of heads per toss `=(sumfx)/N`

`=2470/1000=2.47`

∴ Mean = 2.47

#### Solution 2

Let the assumed mean (A) = 2

No. of heads per toss (x_{1}) |
No. of intervals (f_{1}) |
u (A = 2) |
f_{1}u_{1} |

0 | 38 | -2 | -76 |

1 | 144 | -1 | +44 |

2 | 342 | 0 | 0 |

3 | 287 | 1 | 287 |

4 | 164 | 2 | 328 |

5 | 25 | 3 | 75 |

N = 1000 | `sumf_1u_1=470` |

Mean number of per toss `=A+(sumf_1u_1)/N`

`=2+470/1000`

= 2 + 0.47

= 2.47

Is there an error in this question or solution?

#### APPEARS IN

Solution Five Coins Were Simultaneously Tossed 1000 Times and at Each Toss the Number of Heads Were Observed. the Number of Tosses During Which 0, 1, 2, 3, 4 and 5 Heads Were Obtained Are Shown Concept: Mean of Grouped Data.