Question

Consider the following sample of numbers: \[ 9, \; 18, \; 11, \; 14, \; 15, \; 17, \; 10, \; 69, \; 11, \; 13 \] The median of the sample is ?

• A. 13.5
• B. 14
• C. 11
• D. 18.7

Hint:

For even-sized data sets, the median is always the average of the middle two values after arranging the data in order.

Answer 1

The Correct Option is A

Step 1: Arrange the numbers in ascending order. \[ 9, \; 10, \; 11, \; 11, \; 13, \; 14, \; 15, \; 17, \; 18, \; 69 \] 

Step 2: Count the total number of observations. There are $n = 10$ observations.

Step 3: Find the median formula for even $n$. For even number of terms, \[ \text{Median} = \frac{\text{Value at } \frac{n}{2} \text{th position + Value at } (\frac{n}{2}+1)\text{th position}}{2} \] 

Step 4: Apply values. Here $n=10$. 

- The $\frac{10}{2} = 5$th value = 13. 

- The $\frac{10}{2} + 1 = 6$th value = 14. 

\[ \text{Median} = \frac{13+14}{2} = \frac{27}{2} = 13.5 \] \[ \boxed{13.5} \]