Answer
(a) Mean=$\bar{x}= 22$
(b) Median= $21 $
(c) Mode= $\text{No Mode}$
Work Step by Step
$$\text{Part (A)}$$
$\text{Given Information:} $
Data Set $\rightarrow (13, 30, 16, 19, 20, 22, 25, 31)$
Total Number of Items in Data Set $n= 8$
To Find: (a) Mean (b) Median (c) Mode
(a) To Find Mean:
Mean $\bar{x} =\frac {13+30+16+19+20+22+25+31}{8}$
$\bar{x} =\frac {176}{8} $
$\bar{x}=22$
(b) To Find Median:
Re-Arrange the Given Data Set in Ascending Order
Data Set $\rightarrow (13, 16, 19, \color{red}{20, 22,} 25, 30, 31 )$
Since there are two centers of measure so, therefore, the $\text{Median}$ is the Mean of the two values:
$\bar{x} =\frac {20+22}{2}$
$\bar{x} =\frac {42}{2}$
$\bar{x} =21$
$\text{Median }= 21$
(c) To Find Mode:
Data Set $\rightarrow (13, 30, 16, 19, 20, 22, 25, 31)$
There is $\text{No Mode}$ as each value in the data set appears once only.
Answer:
(a) Mean=$\bar{x}= 22$
(b) Median= $21 $
(c) Mode= $\text{No Mode}$
$$\text{Part (B)}$$
The $\text{Mean}$ best represents the data because there are $\text{NO}$ outliers.
