#### Question

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 batsmen |

3000 − 4000 | 4 |

4000 − 5000 | 18 |

5000 − 6000 | 9 |

6000 − 7000 | 7 |

7000 − 8000 | 6 |

8000 − 9000 | 3 |

9000 − 10000 | 1 |

10000 − 11000 | 1 |

Find the mode of the data.

#### Solution

From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 − 5000.

Therefore, modal class = 4000 − 5000

Lower limit *(l*) of modal class = 4000

Frequency (*f*_{1}) of modal class = 18

Frequency (*f*_{0}) of class preceding modal class = 4

Frequency (*f*_{2}) of class succeeding modal class = 9

Class size (*h*) = 1000

`"Mode" = l + ((f_1-f_0)/(2f_1-f_0-f_2))xxh`

= `4000+((18-4)/(2(18)-4-9))xx1000`

= `4000+(14000/23)`

= 4000+608.695

= 4608.695

Therefore, mode of the given data is 4608.7 runs.

Is there an error in this question or solution?

Solution The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches Concept: Mode of Grouped Data.