Question

Marks obtained by 100 students in an examination are given in the table:

Sl. No.	Marks obtained	Number of students
1	25	20
2	30	20
3	35	40
4	40	20

What would be the mean, median and mode of the marks obtained by the students?

• A. Mean 33; Median 35; Mode 40
• B. Mean 35; Median 32; Mode 40
• C. Mean 33; Median 35; Mode 35
• D. Mean 35; Median 32; Mode 35

Answer 1

The correct option is C Mean 33; Median 35; Mode 35

Given that total number of students
= 100 = N (let)
Mean (Av. Marks)$=\frac{\text{Total Marks obtained}}{\text{Total students}}$

$=\frac{(20\times 25)+(20\times 30)+(40\times 35)+(20\times 40)}{(20+20+40+20)}$

$=\frac{500+600+1400+800}{100}$

$=\frac{3300}{100}=33$

$Median=\frac{{\left(\frac{N}{2}\right)}^{th}Marks+{(\frac{N}{2}+1)}^{th}Marks}{2}$
= The average marks of 50th, 51th observations

$=\frac{35+35}{2}=35$

Mode = The value of marks with highest frequency = 35

(because 35 marks are obtained by most number of students)