Count observations

Count the number of observations $n$ in the given list: 29, 32, 48, 50, $x$, $2x+3$, 72, 78, 84, 95. There are $n = 10$ observations.

$n = 10$

Identify median formula

Since $n$ is even, the median is the arithmetic mean of the $(\frac{n}{2})^{th}$ and $(\frac{n}{2} + 1)^{th}$ terms.

$\text{Median} = \frac{5^{th} \text{ term} + 6^{th} \text{ term}}{2}$

Apply values

The 5th term is $x$ and the 6th term is $2x + 3$. Given the median is 63:

$\frac{x + (2x + 3)}{2} = 63$

Solve for x

Multiply both sides by 2 and solve the linear equation: $3x + 3 = 126$, which leads to $3x = 123$.

$x = \frac{123}{3} = 41$