Question

Find the median of first 6 multiples of 5.

• A. 7.5
• B. 17.5
• C. 27.5
• D. 37.5

Hint:

For an Arithmetic Progression with an even number of terms, the median is always exactly halfway between the two central numbers.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The median is the middle value of a sorted data set. For an even number of observations ($n$), the median is the average of the two middle terms: the $(n/2)^{th}$ and $(n/2 + 1)^{th}$ terms.

Step 2: Key Formula or Approach:
First 6 multiples of 5 are: $5, 10, 15, 20, 25, 30$. Since $n=6$ (even), \[ \text{Median} = \frac{(\text{Value at } 3^{rd} \text{ position} + \text{Value at } 4^{th} \text{ position})}{2} \]

Step 3: Detailed Explanation:
The sorted multiples are $5, 10, 15, 20, 25, 30$. The $3^{rd}$ term is 15. The $4^{th}$ term is 20. \[ \text{Median} = \frac{15 + 20}{2} \] \[ \text{Median} = \frac{35}{2} = 17.5 \]

Step 4: Final Answer:
The median of the first 6 multiples of 5 is 17.5.