The table below summarises the calculation for the standard deviation of x-bar.
[tex]\begin{tabular}
{|c|c|c|c|}
Drawing (x)&$\bar{x}${data-answer}amp;$x-\bar{x}${data-answer}amp;$(x-\bar{x})^2\\[1ex]
2,2,2&2&-2.5&6.25\\
2,2,3&2.3&-2.2&4.84\\
2,2,5&3&-1.5&2.25\\
2,2,8&4&-0.5&0.25\\
2,3,3&2.7&-1.8&3.24\\
2,3,5&3.3&-1.2&1.44\\
2,3,8&4.3&-0.2&0.04\\
2,5,5&4&-0.5&0.25\\
2,5,8&5&0.5&0.25\\
2,8,8&6&1.5&2.25\\
3,3,3&3&-1.5&2.25\\
3,3,5&3.7&-0.8&0.64\\
3,3,8&4.7&0.2&0.04\\
3,5,5&4.3&-0.2&0.04\\
3,5,8&5.3&0.8&0.64\\
3,8,8&6.3&1.8&3.24\\
5,5,5&5&0.5&0.25\\
5,5,8&6&1.5&2.25\\
5,8,8&7&2.5&6.25\\
8,8,8&8&3.5&12.25\\
\end{tabular}[/tex]
[tex]\sum\bar{x}=89.9 \\ \\ \bar{\bar{x}}= \frac{\sum\bar{x}}{n}=\frac{89.9}{20} \approx4.5 \\ \\ \sum(x-\bar{x})^2=30.41 \\ \\ s.d= \sqrt{ \frac{\sum(x-\bar{x})^2}{n} } = \sqrt{ \frac{30.41}{20} } = \sqrt{1.5205} =1.23[/tex]
Therefore, the standard deviation of x-bar is approximately 1.23.
