The standard deviation of the first 10 natural numbers is 3.028. What will be the standard deviation of the first 20 natural numbers? 

This question was previously asked in
SSC CGL Tier-II (JSO) 2022 Official Paper (Held On: 4 March 2023)
View all SSC CGL Papers >
  1. 7.525
  2. 5.845
  3. 3.028
  4. 9.325

Answer (Detailed Solution Below)

Option 2 : 5.845
super-pass-live
Free
SSC CGL Tier 1 2025 Full Test - 01
3.5 Lakh Users
100 Questions 200 Marks 60 Mins

Detailed Solution

Download Solution PDF
The correct answer is 5.845
 Key PointsThe standard deviation of the first 10 natural numbers: 
Formula: \(σ = \sqrt {{(n^2 - 1)}\over 12}\); where, σ = standard deviation, n = sample size 
Or, σ = \(\sqrt{(20^2 - 1) \over 12} = 5.766 \approx 5.8\)
This is closest to 5.845 
Hence, the standard deviation of the first 20 natural numbers is 5.845.
Important Points The standard deviation of a set of numbers is a measure of the amount of variance or dispersion among the numbers. It doesn't scale linearly or predictably with the number of elements in the set, or with the standard deviation of a different set of numbers. Therefore, the standard deviation of the first 20 natural numbers can't be calculated directly from the standard deviation of the first 10 natural numbers. 
Latest SSC CGL Updates

Last updated on Jul 16, 2025

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.

-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.

-> The CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> The Bihar Sakshamta Pariksha Admit Card 2025 for 3rd phase is out on its official website.

Get Free Access Now
Hot Links: teen patti joy apk teen patti bindaas teen patti neta teen patti master teen patti bonus