Question

The mean of the data $:16,19,20,19,X,21,26,20$ is $20$. if the mode is $x$ and the median is $y,$ then the value of $y^2-x^2$ is

• A. $19$
• B. $19.25$
• C. $zero$
• D. $20.50$

Answer 1

The correct option is B $19.25$

The given numbers are $16,19,20,19,x,21,26,20$

Number of observations $=8$

$\Rightarrow$ $Mean=\frac{16+19+20+19+x+21+26+20}{8}$

$\Rightarrow$ $20=\frac{141+x}{8}$

$\Rightarrow$ $160=141+x$

$\Rightarrow$ $x=19$

Now, arranging given number in ascending order,

$16,19,19,19,20,20,21,26$

$Median=\frac{4^{th}obs+5^{th}obs}{2}$

$\therefore$ $Median=\frac{19+20}{2}=\frac{39}{2}=19.5$

$\therefore$ $y=19.5$

$\Rightarrow$ $y^2-x^2=(19.5{)}^2-(19{)}^2=380.25-361=19.25$