No. To compute the median, you arrange the whole dataset in increasing order, and pick the element in the middle. So, you have [tex] N [/tex] observations so far, you write the dataset as
[tex] x_1,\ x_2,\ x_3,\ldots,x_{\frac{N}{2}-1},\ x_{\frac{N}{2}},\ x_{\frac{N}{2}+1},\ldots, x_N [/tex]
And the median is the element in the middle, i.e [tex] x_{\frac{N}{2}}[/tex]
Now, assume you add the last observation, [tex]x_{N+1} [/tex]. This is much larger than the rest of the dataset, so if we arrange the dataset in increasing order, it will be the last:
[tex] x_1,\ x_2,\ x_3,\ldots,x_{\frac{N}{2}-1},\ x_{\frac{N}{2}},\ x_{\frac{N}{2}+1},\ldots, x_N,\ x_{N+1} [/tex]
But the median is always the element in the middle, so it is again either [tex] x_{\frac{N}{2}} [/tex] or [tex] x_{\frac{N+1}{2}} [/tex]
