If $u_i=\frac{x_i-25}{10}$, $\sum f_i{u}_i=20$, and $\sum f_i=100$, then find the value of the mean $\bar{x}$.

The given equation for $u_i$ matches the standard step-deviation format:
$$u_i=\frac{x_i-A}{h}$$

By comparing terms:

* Assumed Mean ($A$) = $25$
* Class width ($h$) = $10$

The formula for calculating the arithmetic mean ($\bar{x}$) using the step-deviation method is:

$$\bar{x}=A+h\times \left(\frac{\sum f_i{u}_i}{\sum f_i}\right)$$

Substitute the given values into the formula:

$$\bar{x}=25+10\times \left(\frac{20}{100}\right)$$

$$\bar{x}=25+10\times 0.2=25+2=27$$