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JEE Main 20208 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2020 · 8 January · Evening Shift · Mathematics · Statistics

The mean and variance of 20 observations are found to be 10 and 4,...

The mean and variance of 2020 observations are found to be 1010 and 4,4, respectively. On rechecking, it was found that an observation 99 was incorrect and the correct observation was 11,11, then the correct variance is

Options

  1. A3.993.99
  2. B4.014.01
  3. C4.024.02
  4. D3.983.98

Correct answer

A. 3.993.99

Step-by-step solution

∑xi20=10…(i)\dfrac{∑ {x}_{i}}{20} = 10 \ldots ( i )
∑xi220−100=4…(ii)\dfrac{∑ {x}_{i}^{2}}{20} - 100 = 4 \ldots ( ii )
∑xi2=104×20=2080∑ {x}_{i}^{2} = 104 \times 20 = 2080
Actual mean =200−9+1120=20220= \dfrac{200 - 9 + 11}{20} = \dfrac{202}{20}
Variance =2080−81+12120−(20220)2= \dfrac{2080 - 81 + 121}{20} - {\left(\dfrac{202}{20}\right)}^{2}
=212020−(10.1)2=106−102.01=3.99= \dfrac{2120}{20} - {\left(10.1\right)}^{2} = 106 - 102.01 = 3.99
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