Question
Download Solution PDFIf the sum of 10 observations is 12 and the sum of their squares is 18, then the standard deviation is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFStandard deviation = \(\sqrt{{{(x_i - \bar x)}^2} \over n} = \sqrt {Variance} \)
Therefore, Variance V(X) = \({1 \over n} {{(x_i - \bar x)}^2} \)
or, \(\rm v(x)=\frac{1}{n}\left[\Sigma(x_i^2-2\times x_i \times \bar x+\bar x^2)\right]\)
\(\rm =\frac{\Sigma x_i^2}{n}-2 \bar x\left(\frac{\Sigma x_i}{n}\right)+\frac{\Sigma \bar x^2}{n}\)
\(=\rm \frac{\Sigma x_i^2}{n}-2\bar x^2+\frac{n.\bar x^2}{n}\)
\(\rm = \frac{\Sigma x_i^2}{n}-2\bar x^2+\bar x^2\)
\(\rm V(x)=\frac{\Sigma x_i^2}{n}-\bar x^2\)
Given, the sum of 10 observations is 12 and the sum of their squares is 18.
Thus, n = 10, \(\sum x_i = 12\), \(\sum x_i^2 = 18\)
Therefore, mean \(\bar x = 1.2\)
Plugging this information into the equation of variance V(X), we have
\(\rm V(x)=\frac{\Sigma x_i^2}{n}-\bar x^2\)
\(=\frac{1}{10}\times 18-(1.2)^2\)
= 1.8 - 1.44
=0.36
Hence, the required standard deviation = \(\sqrt {Variance} = \sqrt{(0.36)} = 0.6 = {3 \over 5}\)
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> 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.
-> Candidates should also use the SSC CGL previous year papers for a good revision.