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# The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored | Number of batsman | Runs scored | Number of batsman |

3000-4000 | 4 | 7000-8000 | 6 |

4000-5000 | 18 | 8000-9000 | 3 |

5000-6000 | 9 | 9000-10000 | 1 |

6000-7000 | 7 | 10000-11000 | 1 |

Find the mode of the data."

Given:

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

To do:

We have to find the mode of the data.

Solution:

The frequency of the given data is as given below.

Runs scored($x_i$): | Number of batsman$(f_i$): |

3000-4000 | 4 |

4000-5000 | 18 |

5000-6000 | 9 |

6000-7000 | 7 |

7000-8000 | 6 |

8000-9000 | 3 |

9000-10000 | 1 |

10000-11000 | 1 |

We observe that the class interval of 4000-5000 has the maximum frequency(18).

Therefore, it is the modal class.

Here,

$l=4000, h=1000, f=18, f_1=4, f_2=9$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=4000+\frac{18-4}{2 \times 18-4-9} \times 1000$

$=4000+\frac{14}{36-13} \times1000$

$=4000+\frac{14000}{23}$

$=4000+608.7$

$=4608.7$

The mode of the given data is 4608.7.