Question 1158372
Range, standard deviation, and variance are measures of the dispersion of the data in a set.
A long time ago, in college, I would calculate them using paper and pen, based on their definitions.
Nowadays, a calculator, or computer software can calculate them for us easily, but we have to understand what this measure tell us and exactly what our devices.
 
Range:
The range is the difference between the smallest and greatest values.
{{{Range=514-458=highlight(56)}}}
 
Variance:
The mean (average) of all 10 values is
{{{(514+507+502+498+496+506+458+478+463+514)/10=4936/10=493.6}}}
The deviations from the mean for the individual values are:
{{{514-493.6=20.4}}} (514 appears twice)
{{{507-493.6=13.4}}}
{{{502-493.6=8.4}}}
{{{498-493.6=4.4}}}
{{{496-493.6=2.4}}}
{{{506-493.6=12.4}}}
{{{458-493.6=-35.6}}
{{{478-493.6=-15.6}}}
{{{463-493.6=-30.6}}}
Their squares are:
{{{20.4^2=416.16}}} (514 appears twice)
{{{13.4^2=179.56}}}
{{{8.4^2=70.56}}}
{{{4.4^2=19.36}}}
{{{2.4^2=5.76}}}
{{{12.4^2=153.76}}}
{{{-35.6^2=1267.36}}
{{{-15.6^2=243.36}}}
{{{-30.6^2=936.36}}}
The variance is the average of those squares: 
{{{(416.16+416.16+179.56+70.56+19.36+5.76+153.76+1267.36+243.36+936.36)/10=3708.4/10=highlight(370.84)}}}
 
Standard deviation:
The standard deviation, as asked in this question, is the square root of the variance as calculated above:
{{{sqrt(370.84)=highlight(19.26)}}} (rounded)
Software that calculates statistics would have to forms of standard deviation:
the standard deviation of a population, calculated as above, and
the standard deviation of a sample, used to estimate the dispersion of the whole population of data based on a sample of N items. In the second case, the sum of squares in divided by N-1 instead.