Question

The distribution given below shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.

Marks obtained	$5$	$6$	$7$	$8$	$9$	$10$
No. of students	$3$	$9$	$6$	$4$	$2$	$1$

Answer 1

Step 1: Make the required table for frequency and the cumulative frequency:

The values of Frequency$\left(f_i{x}_i\right)$ and Cumulative Frequency $\left(\mathrm{CF}\right)$ are written below,

Marks obtained $\left(x_i\right)$	No. Of Students $\left(f_i\right)$	Frequency$\left(f_i{x}_i\right)$	Cumulative Frequency$\left(CF\right)$
$5$	$3$	$15$	$3$
$6$	$9$	$54$	$12$
$7$	$6$	$42$	$18$
$8$	$4$	$32$	$22$
$9$	$2$	$18$	$24$
$10$	$1$	$10$	$25$
	$\sum _{}{f}_i=25$	$\sum _{}{f}_i{x}_i=171$

Frequency $=$Marks obtained $\times$No. of Student

To find the cumulative frequency $=$Cumulative Frequency$+$ Frequency

Step 2: Find the value of the mean.

Mean $=\frac{\sum _{}{f}_i{x}_i}{\sum _{}{f}_i}$

Mean $=\frac{171}{25}$

Mean $=6.84$

Step 3: Find the value of the Median.

Median $=\frac{\sum _{}{f}_i+1}{2}$

Median $=\frac{25+1}{2}$

Median $=\frac{26}{2}$

Median $=13th$

Now, check the Cumulative Frequency.

Since$13$ is more than $12$ and less then$18$.

Therefore, the number corresponding to 18 in the marks obtained $\left(x_i\right)$ column is the median.

So, Median $=7$

Step 4: Find the value of the mode.

Mode is a value that occurs most often in the list.

From the table, $6$ marks are obtained by $9$ students, which is the highest.

So, the value of the mode is $6.$

Hence, Mean is$6.84$, Median is $7$ and Mode is $6.$