Question

Calculate the mean, median and mode of the following distribution

No. of goals	$0$	$1$	$2$	$3$	$4$	$5$
No. of students	$2$	$4$	$7$	$6$	$8$	$3$

Answer 1

Prepare table for the values of Frequency$\left(F\right(x\left)\right)$ and Cumulative Frequency $\left(CF\right)$

No. of Goals	No. of Students $\mathbf{\left(}\mathit{F}\mathbf{\right)}$	Frequency$\left(F\right(x\left)\right)$	Cumulative Frequency$\left(CF\right)$
$0$	$2$	$0$	$2$
$1$	$4$	$4$	$6$
$2$	$7$	$14$	$13$
$3$	$6$	$18$	$19$
$4$	$8$	$32$	$27$
$5$	$3$	$15$	$30$
	$\sum F=30$	$\sum F\left(x\right)=83$

Step 2:Find the value of mean.

Mean $=\frac{\sum _{}F\left(x\right)}{\underset{}{\sum F}}$

Mean $=\frac{83}{30}$

Mean $=2.767$

Step 3: Find the value of Median.

Median $=\frac{F+1}{2}$

Median $=\frac{30+1}{2}$

Median $=\frac{31}{2}$

Median$=15.50$

Since, $15.50$ is greater than 13 and less than 19.

So, we will take the no. of goals corresponding to the cumulative frequency 19.

Therefore, Median $=3$

Step 4:Find the value of mode:

Mode is the value that occurs most often in the given number of sets.

Since $4$ goals are scored by a maximum number of students.

Therefore, the value of mode is $4$.

Hence, the mean, median, and mode of the following distribution is $2.767$, $3$ and$4$ respectively.