Question 724051
1). Arithmetic {{{Mean (Average) = (14 +5+ 17 +2 +10 +23 +19+ 8+ 7) /  9=105/9=11.67}}}

2). Variance 
The variance is calculated as the average squared difference between each number and the mean.

variance  ={{{ ((14-11.67)^2 + (5-11.67)^2 + (17-11.67)^2+ (2-11.67)^2+(10-11.67)^2+(23-11.67)^2+(19-11.67)^2+(8-11.67)^2+(7-11.67)^2) /  9 }}}

= {{{((2.33)^2 + (-6.67)^2 + (5.33)^2+ (-9.67)^2+(-1.67)^2+(11.33)^2+(7.33)^2+(-3.67)^2+(-4.67)^2) /  9 }}}

= {{{(16 + 25 + 49+ 64+0+169+81+4+9) /  9 }}}

={{{392/9=43.56}}}

The standard deviation is the square root of the variance. 

{{{sqrt(43.56)=6.6}}}

If a normal distribution, 1 standard deviation from the mean is ±{{{6.6}}} which means 68% of values should fall between {{{5.07}}} and {{{18.27}}}


 range: {{{2}}} to {{{23}}} ={{{22}}} (inclusive)