Consider the following sample of numbers:
9, 18, 11, 14, 15, 17, 10, 69, 11, 13
The median of the sample is
Options:
(A) 13.5
(B) 14
(C) 11
(D) 18.7
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2024 Q.3)**
**1. Governing Concept**:
- **Topic**: Numerical Ability & Descriptive Statistics (Median)
- The sample consists of $n = 10$ numbers: $9, 18, 11, 14, 15, 17, 10, 69, 11, 13$.
- Arranging in ascending order:
$9, 10, 11, 11, 13, 14, 15, 17, 18, 69$
- For an even number of observations ($n = 10$), the median is the average of the 5th and 6th terms:
$\text{Median} = \frac{x_5 + x_6}{2} = \frac{13 + 14}{2} = 13.5$
**2. Option Analysis**:
- **Option (A) [13.5] is CORRECT**: Exactly matches $\frac{13 + 14}{2} = 13.5$.
- **Option (B) [14] is INCORRECT**: Represents the 6th value alone without averaging.
- **Option (C) [11] is INCORRECT**: Represents the sample mode, not the median.
- **Option (D) [18.7] is INCORRECT**: Represents the sample arithmetic mean ($\frac{187}{10} = 18.7$), which is heavily distorted by the outlier 69.
**3. Final Answer**:
- **Correct Choice**: **A**
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