Test Index

UPSC NDA I 2026 Mathematics Paper

Question Numbers: 119-120

For the next two (02) items that follow:

The frequency distribution of marks obtained by 100 students in a certain subject is given below :

Marks	0-10	10-20	20-30	30-40
No. of students	10	20	f	40

Question : 119 of 120

Marks: +1, -0

What is the mean deviation about the arithmetic mean ?

Solution:

Concept:

Mean deviation about the arithmetic mean is

\frac{\sum f_i |x_i - \bar{x}|}{\sum f_i}

Explanation:

Total students

= 100

10 + 20 + f + 40 = 100 \Rightarrow f = 30

Class marks are

5, 15, 25, 35

Mean

\bar{x} = \frac{10(5)+20(15)+30(25)+40(35)}{100}

\bar{x} = \frac{2500}{100} = 25

Mean deviation

= \frac{10|5-25|+20|15-25|+30|25-25|+40|35-25|}{100}

= \frac{200+200+0+400}{100} = \frac{800}{100} = 8

Answer:

Option D:

8

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