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 40 What is the standard deviation? किसी विषय में 100 छात्रों द्वारा प्राप्तांकों का बारंबारता बंटन नीचे दिया गया है : अंक 0-10 10-20 20-30 30-40 छात्रों की संख्या 10 20 40 मानक विचलन क्या है ?

Explanation: 1. Determine the Missing Frequency ( ) The total number of students is . We sum the frequencies to find : 2. Construct the Frequency Table to Find the Mean ( ) We calculate the midpoint ( ) for each class interval and determine the arithmetic mean. Marks Frequency (fi) Midpoint (xi) fi⋅xi 0-10 10-20 20-30 30-40 Calculating the sum of frequencies ( ) and the sum of products ( ): 3. Calculate the Variance ( ) and Standard Deviation ( ) We use the formula for variance: . xi (xi−xˉ)2 fi fi(xi−xˉ)2 Summing the squared deviations: Calculating the standard deviation: Correct Option: (d) 10

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NDA 2026 — Mathematics PYQ

NDA | Mathematics | 2026

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

What is the standard deviation?

किसी विषय में 100 छात्रों द्वारा प्राप्तांकों का बारंबारता बंटन नीचे दिया गया है :

अंक	0-10	10-20	20-30	30-40
छात्रों की संख्या	10	20	$f$	40

मानक विचलन क्या है ?

Marks	Frequency (fi)	Midpoint (xi)	fi⋅xi
0-10	$10$	$5$	$50$
10-20	$20$	$15$	$300$
20-30	$30$	$25$	$750$
30-40	$40$	$35$	$1400$

xi	(xi−xˉ)2	fi	fi(xi−xˉ)2
$5$	$(5 - 25)^{2} = 400$	$10$	$4000$
$15$	$(15 - 25)^{2} = 100$	$20$	$2000$
$25$	$(25 - 25)^{2} = 0$	$30$	$0$
$35$	$(35 - 25)^{2} = 100$	$40$	$4000$

Marks	Frequency (fi)	Midpoint (xi)	fi⋅xi
0-10	$10$	$5$	$50$
10-20	$20$	$15$	$300$
20-30	$30$	$25$	$750$
30-40	$40$	$35$	$1400$

xi	(xi−xˉ)2	fi	fi(xi−xˉ)2
$5$	$(5 - 25)^{2} = 400$	$10$	$4000$
$15$	$(15 - 25)^{2} = 100$	$20$	$2000$
$25$	$(25 - 25)^{2} = 0$	$30$	$0$
$35$	$(35 - 25)^{2} = 100$	$40$	$4000$

Choose the correct answer: