Question

Calculate Mean, Median and Mode for the following data. Which of these three measures if minimum?

Marks s(out of 15)

$7$

$4$

$10$

$9$

$15$

$12$

$7$

$9$

$9$

Answer 1

Arranging given marks in ascending order,

$4,7,7,9,9,9,10,12,15$

Number of observations $\left(n\right)=9$

$\Rightarrow$ $Mean=\frac{4+7+7+9+9+9+10+12+15}{9}=\frac{82}{9}=9.11$

$\Rightarrow$ Here, number $9$ occurs maximum number of times i.e $3$ times.

$\therefore$ $Mode=9$

Number of observation is odd number

$\therefore$ $Median={\left(\frac{n+1}{2}\right)}^{th}obs={\left(\frac{9+1}{2}\right)}^{th}obs=5^{th}obs$

Here, $5^{th}obs=9$

$\therefore$ $Median=9$

$\Rightarrow$ So, we can see $mean$ measure is maximum and $mode,median$ measures are minimum.