Question

For the following frequency distribution find:
(i) Lower quartile
(ii) Upper quartile
(iii) Inter quartile range
(iv) Semi-inter quartile range.

| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| y | 3 | 5 | 9 | 15 | 20 | 16 | 10 | 2 |

Answer 1

| 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.