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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 : 120 of 120

Marks: +1, -0

What is the standard deviation?

Solution:

Concept:

Use grouped data formula:

\sigma = \sqrt{\frac{\sum f_i (x_i - \bar{x})^2}{N}}

Explanation:

Total students

= 100

, so

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

Class marks are

5, 15, 25, 35

with frequencies

10, 20, 30, 40

Mean:

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

Variance:

\sigma^2 = \frac{10(-20)^2 + 20(-10)^2 + 30(0)^2 + 40(10)^2}{100} = 100

Standard deviation:

\sigma = \sqrt{100} = 10

Answer:

10

, i.e. option D.

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