| **x** | **f** | **Cumulative frequency** |

| 1 | 3 | 3 |

| 2 | 5 | 8 |

| 3 | 9 | 17 |

| 4 | 15 | 32 |

| 5 | 20 | 52 |

| 6 | 16 | 68 |

| 7 | 10 | 78 |

| 8 | 2 | 80 |

| | | **n = 80** |

(i) Lower quartile

(Q1) = The value of $("n"/4)^"th"$ observation

= The value of $(80/4)^"th"$ observation

= The value of 20th observation

Q1 = 4.

(ii) Upper quartile

(Q3) = The value of $((3"n")/4)^"th"$ observation

= The value of $((3 xx 80)/4)^"th"$ observation

= The value of 60th observation

Q3 = 6.

(iii) Inter quartile range

= Q3 - Q1

= 6 - 4

= 2.

(iv) Semi-quartile range

= $(Q_3 - Q_1)/(2)$

= $(2)/(2)$

= 1.