Answer
See below
Work Step by Step
The mean, median, mode, range, and standard deviation of the data set when the outlier is included:
$\bar x=\frac{22.2+22.5+22.5+23+23.61+23.61+24.5+24.8+25.3+25.7+26.2+27.72}{12}=24.33\\ Median =\frac{23.61+24.5}{2}=24.08\\Mode =23.61\\Range=27.72-22.2=5.5\\\sigma =1.64$