Answer
(a) Mean $\bar{x}= 13.2$
(b) Median= $14.5 $
(c) Mode= $\text{14 and 15}$
Work Step by Step
$$\text{Part (A)}$$
$\text{Given Information:} $
Data Set $\rightarrow (14, 15, 3, 15, 14, 14, 18, 15, 8, 16)$
Total Number of Items in Data Set $n= 10$
To Find: (a) Mean (b) Median (c) Mode
(a) To Find Mean:
Mean $\bar{x} =\frac {14+15+3+14+14+18+15+8+16}{10}$
$\bar{x} =\frac {132}{10} $
$\bar{x}=13.2$
(b) To Find Median:
Re-Arrange the Given Data Set in Ascending Order
Data Set $\rightarrow (3, 8, 14, 14, \color{red}{14, 15,} 15, 15, 16, 18 ) $
Since there are two centers of measure so, therefore, the $\text{Median}$ is the Mean of the two values:
$\bar{x} =\frac {14+15}{2}$
$\bar{x} =\frac {29}{2}$
$\bar{x} =14.5$
$\text{Median }= 14.5$
(c) To Find Mode:
Data Set $\rightarrow(\color{red}{14, 15}, 3, \color{red}{15, 14, 14,} 18, \color{red}{15}, 8, 16 )$
There are two modes $\text{14 and 15}$ as they occur more than once in the data set.
Answer:
(a) Mean=$\bar{x}= 13.2$
(b) Median= $14.5 $
(c) Mode= $\text{14 and 15}$
$$\text{Part (B)}$$
The $\text{Median}$ best represents the data because the outlier disturbs the Mean.
