Q26: The diameter at breast height (DBH) of $20$ trees are... - Statistical Methods & Experimental Designs - ICAR AIEEA PG Statistical Science 14 July 2023 Shift-1 Paper | Agrigyan

Calculation of quartiles for $n = 20$ sorted observations:

• The sorted values are: $1, 3, 5, 5, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10$.
• The first quartile $Q_1$ lies between the $5^{\text{th}}$ observation ($7$) and $6^{\text{th}}$ observation ($8$), yielding $Q_1 = 7.5$.
• The median $Q_2$ is the average of the $10^{\text{th}}$ ($8$) and $11^{\text{th}}$ ($8$) observations, giving $Q_2 = 8$.
• The third quartile $Q_3$ lies between the $15^{\text{th}}$ observation ($9$) and $16^{\text{th}}$ observation ($9$), giving $Q_3 = 9$. Hence, $Q_1 = 7.5, Q_2 = 8, Q_3 = 9$.