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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Statistics

JEE Main 2017 · 9 April · Online · Mathematics · Statistics

The sum of 100 observations and the sum of their squares are 400...

The sum of 100100 observations and the sum of their squares are 400 and 2475400 \text{ and } 2475, respectively. Later on, three observations 3,4 and 53, 4 \text{ and } 5 were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is

Options

  1. A8.258 . 25
  2. B8.508 . 50
  3. C9.009 . 00
  4. D8.008 . 00

Correct answer

C. 9.009 . 00

Step-by-step solution

Given ∑i=110xi=400\mathop{∑}_{i = 1}^{10}{x}_{i} = 400 and

∑i=1100xi2=2475\mathop{∑}_{i = 1}^{100}{{x}_{i}}^{2} = 2475

Variance of 9797 observations=σ2=∑xi2N−(∑xiN)2= {\sigma}^{2} = \dfrac{∑ {{x}_{i}}^{2}}{N} - {\left(\dfrac{∑ {x}_{i}}{N}\right)}^{2}

\left(∴ 3 + 4 + 5 = 12, {3}^{2} + {4}^{2} + {5}^{2} = 50\right)<br/><br/><br /><br />= \dfrac{2425}{97} - {\left(\dfrac{388}{97}\right)}^{2}<br/><br/><br /><br />= \dfrac{2425}{97} - 16<br/><br/><br /><br />= \dfrac{2425 - 1552}{97} = \dfrac{873}{97}<br/><br/><br /><br />= 9$

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