Biomolecules, enzyme kinetics

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.32)** **1. Governing Concept & Definition**: - **Topic**: Statistics & Median of Discrete Data - To find the median of a finite numerical dataset with an even number of elements $n = 2m$, sort the elements in ascending order and compute the arithmetic average of the two middle elements at positions $m$ and $m + 1$: $\text{Median} = \frac{x_{(m)} + x_{(m+1)}}{2}$ **2. Detailed Step-by-Step Calculation**: - **Given Raw Dataset**: $\{12, 10, 16, 8, 90, 50, 30, 24\}$ ($n = 8$ elements) - **Sorted Dataset (Ascending)**: $8, 10, 12, \mathbf{16}, \mathbf{24}, 30, 50, 90$ - **Middle Elements ($4^{\text{th}}$ and $5^{\text{th}}$ elements)**: - $x_{(4)} = 16$ - $x_{(5)} = 24$ - **Median Calculation**: $\text{Median} = \frac{16 + 24}{2} = \frac{40}{2} = 20$ **3. Final Answer**: - **Calculated Value**: **20** - **Official GATE Accepted Range**: **20 to 20**