$1,x,x,x,y,y,9,16,18$
The mean
$$\bar{x}=\dfrac{\sum x}{N}$$
Here,
- $\sum$ represents the summation
- $x$ represents scores
- $N$ represents number of scores
Mean $=\dfrac{1+x+x+x+y+y+9+16+18}{9}=\dfrac{3x+2y+44}{9}$
The Median
$(1)$ If the total number of numbers$(n)$ is an odd number, then the formula is given below$:$
$\text Median=\left(\dfrac{n+1}{2}\right)^{th}\text{term}$
$(2)$ If the total number of numbers(n) is an even number , then the formula is given below$:$
$\text Median=\dfrac{\left(\dfrac{n}{2}\right)^{th}\text{term}+\left(\dfrac{n}{2}+1\right)^{th}\text{term}}{2}$
Here in our question $n=9,$ which is odd. So, we apply the first formula and get the median
Write sequence in ascending or descending order
$1,x,x,x,y,y,9,16,18$
Median $=\left(\dfrac{9+1}{2}\right)^{th}\text{term}=\left(\dfrac{10}{2}\right)^{th}\text{term}=5^{th}$ $\text{term}$
Median $=y$
The Mode
The mode is the most frequency occurring score or value.
$1,x,x,x,y,y,9,16,18$
Here mode $=x$
According to the question
$\dfrac{3x+2y+44}{9}=y$
$\implies3x+2y+44=9y$
$\implies 3x-7y=-44\qquad \to (1)$
and $y=2x\qquad \to (2)$
From $(1)$ and $(2)$ we get
$3x- 14x=-44$
$\implies -11x=-44$
$\implies x=4$
$y=2x=2\times 4 =8$
The correct answer is $(D)$