Question

For \( x>0 \), if the variable takes discrete values \( x+4, x+3.5, x+2.5, x-3, x-2, x+0.5, x-0.5, x+5 \), then the value of median is:

• A. \( x - 1.25 \)
• B. \( x - 0.5 \)
• C. \( x + 0.5 \)
• D. \( x + 1.25 \)

Hint:

For a set of data with an even number of values, the median is the average of the two middle values. Ensure to first arrange the data in increasing order.

Answer 1

The Correct Option is B

Step 1: Organize the data in increasing order.
The given values are: \[ x + 4, x + 3.5, x + 2.5, x - 3, x - 2, x + 0.5, x - 0.5, x + 5 \] Arranging these values in increasing order: \[ x - 3, x - 2, x - 0.5, x + 0.5, x + 2.5, x + 3.5, x + 4, x + 5 \] Step 2: Find the median.
Since there are 8 values (even number of values), the median is the average of the 4th and 5th values in the ordered list. The 4th value is \( x + 0.5 \) and the 5th value is \( x + 2.5 \). The median is given by the average of these two values: \[ {Median} = \frac{(x + 0.5) + (x + 2.5)}{2} = \frac{2x + 3}{2} = x + 1.25 \] Step 3: Conclusion.
Thus, the median is \( x + 1.25 \), corresponding to option (4).