Question

Observations of a data are $16,72,0,55,65,55,10,$ and $41$. Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?

Answer 1

Arranging the data in ascending order

$0$,$10$,$16$,$41$,$55$,$55$,$65$,$72$

Here $n=8$

Median $=$ mean of ${\left(\frac{n}{2}\right)}^{th}$ and ${\left(\frac{n}{2}+1\right)}^{th}$ observations

$=$mean of ${\left(\frac{8}{2}\right)}^{th}$ and ${\left(\frac{8}{2}+1\right)}^{th}$ observation

$=$mean of ${\left(4\right)}^{th}$ and ${\left(5\right)}^{th}$ observations

$=$ $\frac{41+55}{2}$

$=$$48$

Mode $=$ $55$

Now, if zero is not taken into consideration

arrange data in ascending order

$0$,$10$,$16$,$41$,$55$,$55$,$65$,$72$

Here $n=7$

Median $={\left(\frac{n+1}{2}\right)}^{th}$

$={\left(\frac{7+1}{2}\right)}^{th}$

$=4^{th}$

$=55$

Mode $=55$

Therefore Mode is correct but Median is wrong