The following observations are arranged in ascending order. If the median of the data is 19, then find the value of x.

6 , 9 , 15 , x + 4 , x + 8 , x + 12 , 30 , 32

Correct option is A

Given:

We are given the following observations in ascending order:

​$$6, 9, 15, x+4, x+8, x+12, 30, 32$$ 

Median = 19  

The total number of observations is 8, as there are 8 values in the list.

For an even number of observations, the median is the average of the two middle values.

Since there are 8 observations, the two middle values are in positions 4 and 5.

The data is ordered as:

​$$6, 9, 15, x+4, x+8, x+12, 30, 32$$ 

$$\text{Thus, the values in positions 4 and 5 are } x+4 \text{ and } x+8.$$ 

The median is the average of the two middle values:

$$\text{Median} = \frac{1}{2} \left( (x+4) + (x+8) \right)$$

$$2 \left( (x+4) + (x+8) \right) = 19$$ 

$$\frac{2x+12}{2} = 19$$ 

$$2x+12=38$$

$$2x=26$$  

​$$x=13$$    

Thus, the value of xxx is 13.​​