The following distribution represents the height of 160 students of a school.

Height (in cm) |
No. of Students |

140 – 145 | 12 |

145 – 150 | 20 |

150 – 155 | 30 |

155 – 160 | 38 |

160 – 165 | 24 |

165 – 170 | 16 |

170 – 175 | 12 |

175 – 180 | 8 |

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:

(1) The median height.

(2) The interquartile range.

(3) The number of students whose height is above 172 cm.

#### Solution

Height (in cm) |
Number of students (f) |
Cumulative Frequency(c.f) |

140-145 | 12 | 12 |

145-150 | 20 | 32 |

150-155 | 30 | 62 |

155-160 | 38 | 100 |

160-165 | 24 | 124 |

165-170 | 16 | 140 |

170-175 | 12 | 152 |

175-180 | 8 | 160 |

N = 160 |

Taking scale as 2 cm=5 cm on an x-axis and 2 cm = 20 students on the y-axis, the Ogive is drawn as below:

1) Median Height = `(N/2)^"th"` value = `(160/2)^"th"` value = 80 th value = 157 cm (Approx)

2) Lower Quartile, `Q_1 = (N/4)^"th"` value = `(160/4)^"th"` value = 40 th value 152 cm

Upper quartile, `Q_3 = ("3N"/4)^"th"` value = `((3xx160)/4)^"th" `value = `120^"th"` value = 164 cm

Inter Quartile Range, `Q_3 - Q_1 = 164 - 152` = 12 cm

3) The number of students whose height is more than 172 cm = 160 – 142 = 18 students.