Question

The runs scored in a cricket match by $11$ players is as follows:$6,15,120,50,100,80,10,15,8,10,15$ Find the mean, mode and median of this data. Are the three same?

Answer 1

Let us first arrange the runs scored in a cricket match by $11$ players in ascending order,

$6,8,10,10,15,15,15,50,80,100,120$

Calculation of Mean

$\mathrm{Mean}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{data}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{all}\mathrm{observations}}{\mathrm{number}\mathrm{of}\mathrm{observations}}$

$$\begin{gathered} =\frac{(6+8+10+10+15+15+15+50+80+100+120)}{11} \\ =\frac{429}{11} \\ =39 \end{gathered}$$

Mode: Mode is the value of the variable which occurs most frequently.

Clearly, 15 occurs a maximum number of times.

Median: The value of the middle-most observation is called the median of the data.

Here ,$n=11,$ which is odd.

Where n is the number of players.

$\begin{array}{rcl}\therefore \mathrm{median}& =& \left(\mathrm{value}\mathrm{of}\frac{\mathrm{n}+1}{2}\mathrm{term}\right)\\ & =& \left(\mathrm{value}\mathrm{of}{6}^{\mathrm{th}}\mathrm{term}\right)\\ & =& 15\end{array}$

Hence, Mean= $39$, Mode= $15$ median=$15$ All values are not equal