Question

Among the following, a value suitable for \(a\) such that the median of \(4,6,a,9,10,19\) will be \(7.5\) is

• A. 6
• B. 7
• C. 8
• D. 10

Hint:

For \(n\) even observations: \[ \boxed{ \text{Median} = \frac{\left(\frac{n}{2}\right)^{\text{th}}+\left(\frac{n}{2}+1\right)^{\text{th}}}{2} } \] Always arrange the data in ascending order before finding the median.

Answer 1

The Correct Option is A

Concept: For an even number of observations, the median is the average of the two middle terms after arranging the data in ascending order.

Step 1: Arrange the observations.
Choose the option \(a=6\). The data become \[ 4,\;6,\;6,\;9,\;10,\;19. \] These are already in ascending order.

Step 2: Find the median.
There are \(6\) observations. Hence, \[ \text{Median} =\frac{\text{3rd term}+\text{4th term}}{2} =\frac{6+9}{2} =\frac{15}{2} =7.5. \] Thus, the required condition is satisfied.

Step 3: Final conclusion.
Therefore, the suitable value of \(a\) is \[ \boxed{6.} \]