Given the ascending data, the mean is calculated as:

$\frac{57+110+112+114+x+118+120+y}{8}=108.5\backslash frac\{57\; +\; 110\; +\; 112\; +\; 114\; +\; x\; +\; 118\; +\; 120\; +\; y\}\{8\}\; =\; 108.5$857+110+112+114+x+118+120+y​=108.5

This leads to:

$57+110+112+114+x+118+120+y=86857\; +\; 110\; +\; 112\; +\; 114\; +\; x\; +\; 118\; +\; 120\; +\; y\; =\; 868$57+110+112+114+x+118+120+y=868

Calculating the sum of the known values gives $611611$611, so:

$x+y=257x\; +\; y\; =\; 257$x+y=257

For the median of $114.5114.5$114.5, since there are 8 values, the median is the average of the 4th and 5th values:

$\frac{114+x}{2}=114.5\Rightarrow 114+x=229\Rightarrow x=115\backslash frac\{114\; +\; x\}\{2\}\; =\; 114.5\; \backslash Rightarrow\; 114\; +\; x\; =\; 229\; \backslash Rightarrow\; x\; =\; 115$2114+x​=114.5⇒114+x=229⇒x=115

Substituting $xx$x into $x+y=257x\; +\; y\; =\; 257$x+y=257:

$115+y=257\Rightarrow y=142115\; +\; y\; =\; 257\; \backslash Rightarrow\; y\; =\; 142$115+y=257⇒y=142

Thus, $y-x=142-115=27y\; –\; x\; =\; 142\; –\; 115\; =\; 27$y−x=142−115=27. The value of $y-xy\; –\; x$y−x is 27.