Question

If the median of the data observations $7,13,48,12,19,54,61,x$ is $25$ and it is given that $29<x<42$, then find the value of $x$:

• A. $21$
• B. $26$
• C. $31$
• D. $36$

Hint:

For an even number of observations, always average the two middle terms after sorting the data.

Answer 1

The Correct Option is C

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 in ascending order. Given that $29<x<42$, the ordered data becomes $$ 7,\;12,\;13,\;19,\;x,\;48,\;54,\;61 $$

Step 2: Use the median formula. There are $8$ observations, so $$ \text{Median} = \frac{\text{4th term}+\text{5th term}}{2} $$ $$ 25=\frac{19+x}{2} $$

Step 3: Solve for $x$. $$ 19+x=50 $$ $$ x=31 $$ Since $29<31<42$, the value is valid. $$ \boxed{x=31} $$