The following is the distribution of height of students of a certain class in a certain city:

Height (in cm): | 160 - 162 | 163 - 165 | 166 - 168 | 169 - 171 | 172 - 174 |

No. of students: | 15 | 118 | 142 | 127 | 18 |

Find the average height of maximum number of students.

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#### Solution

Height(exclusive) | Height(inclusive) | No. of students |

160 - 162 | 159.5-162.5 | 15 |

163 - 165 | 162.5-165.5 | 118 |

166 - 168 | 165.5-168.5 | 142 |

169 - 171 | 168.5-171-.5 | 127 |

172 - 174 | 171.5-174.5 | 18 |

Here the maximum frequency is 142, then the corresponding class 165.5 – 168.5 is modal class

L = 165.5, h = 168.5 – 165.5 = 3, f = 142, f1 = 118, f2 = 127

Mode `rArr=l+(f-f1)/(2f-f1-f2)xxh`

`=165.5+(142-118)/(2xx142-118-127)xx3`

`=165.5+(24xx3)/39`

`= 165.5 + 72/39`

= 165.5 + 1.85

= 167.35 cm

Concept: Mode of Grouped Data

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