Answer
(a) Mean= $\bar{x}=4$
(b) Median=$ 3$
(c) Mode= $1$
Work Step by Step
$$\text{Solution}$$
$\text{Part (A)}$
$\text{Given Information:}$
Data Set $\rightarrow$ $(3,5,1,5,1,1,2,3,15)$
Total Number of Items in Data Set $\rightarrow$ $n=9$
To Find:
(a) Mean
(b) Median
(c) Mode
(a) To Find Mean:
Mean $\bar{x} =\frac {3+5+1+5+1+1+2+3+15}{9}$
$\bar{x} =\frac {36}{9}$
$\bar{x} =4$
(b) To Find Median:
Re-Arrange the Given Data Set in Ascending Order
Data Set $\rightarrow$ $(1,1,1,2,\color{red}3,3,5,5,15)$
$\text{Median} = 3$ (Since The Middle Value is $3$)
(c) To Find Mode:
Data Set $\rightarrow$ $(3,5,\color{red}1,5,\color{red}1,\color{red}1,2,3,15)$
The $\text{Mode}$ is $1$ as it occurs the most often in the data set.
Answer:
(a) Mean= $\bar{x}=4$
(b) Median=$ 3$
(c) Mode= $1$
$$Part (B)$$
The $\text{Median}$ best represents the data. The $\text{Mean}$ is greater than most of the data and the $\text{Mode}$ is less than the most of data.
