Re: why melting temp of sterling silver is given as range & not exact?

Pure elements generally have specific, well defined properties such as 
melting points.  Pure molecular compounds often also have well defined 
melting points.  Indeed, the triple point of water (the temperature at 
which H2O exists simultaneously as a gas, liquid, and water) is a basis of 
calibrating most temperature scales.

Once you get combinations of elements, however, melting points can start 
acting funny.  Particularly with metals, the elements start to interact 
with each other.  As long as one metal has some solubility in the other, 
you can expect to have changes in melting points compared to what is 
observed for pure metals.  Sterling silver is a compound consisting of 
about 5% copper 
in 95% silver, and is a good example of how complicated melting points can 
become.

In a mixture of two elements, usually called a binary mixture, the behavior 
of the compound as a function of composition and temperature is presented 
in a "phase diagram."  http://cyberbuzz
.gatech.edu/asm_tms/phase_diagrams/ 
presents a large number of phase diagrams for different binary combinations 
of metals.  They present the phase diagram of silver and copper at  http
://cyberbuzz.gatech.edu/asm_tms/phase_diagrams/pd/ag_cu.gif . 

Attached to this answer is the same phase diagram that I have modified in 
order to attempt to answer your question.
  

I have drawn a vertical line at the 5% Cu composition.  This line represents the 
composition of sterling silver.

According to this diagram, as a lump of sterling silver is heated, nothing 
much happens until the temperature reaches about 760oC or so.  Above that 
temperature, the sterling silver starts to melt.  The phase diagram shows 
us that the composition of the material that first melts contains 28.1% 
copper (and 71.9% silver), while that portion of the lump which hasn't 
melted is essentially pure silver.  As the mixture is heated to about 
800oC, the green line shows that the liquid portion of the mixture now has 
a composition of roughly 20% copper, with the solid phase still consisting 
of essentially pure silver.  At 900oC, the liquid phase contains about 8% 
copper (as more and more silver has dissolved into the liquid phase) but 
still contains some solid silver. Not until the temperature reaches 930 or 
940oC has all of the silver dissolved into the liquid phase.

In metal alloys (or combinations of metals) it is typical to list the 
temperature at which the metal alloy first begins to melt (the solidus) and 
the temperature at which the last bit of metal finally dissolves into the 
liquid phase (the liquidus).  You can also understand that if the 
manufacturer of a metal alloy has a little bit of variation when he makes 
up each batch of alloy, there may be some variation in liquidus and solidus 
temperatures.  Because in our specific phase diagram the solidus line is a 
straight horizontal line at 779.1oC, varying the composition of this 
particular alloy will not change the solidus temperature, only the liquidus 
temperature.

I hope this helps you understand a rather complex subject.  It isn't easy.