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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

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

The mean and variance of 1010 observations are found to be 1010 and 44 respectively. On rechecking it was found that an observation 88 was incorrect. If it is replaced by 18,18, then the correct variance is

Options

  1. A77
  2. B88
  3. C99
  4. D556\dfrac{55}{6}

Correct answer

C. 99

Step-by-step solution

x¯(old)=10=Σxi10⇒Σxi(old)=100\overset{¯}{x}\left(old\right) = 10 = \dfrac{Σ{x}_{i}}{10} ⇒ Σ{x}_{i\left(old\right)} = 100
Σxi(new)=100−8+18=110Σ{x}_{i\left(new\right)} = 100 - 8 + 18 = 110
x¯(new)=11010=11\overset{¯}{x}\left(new\right) = \dfrac{110}{10} = 11
Var\left(old\right) = 4 = \dfrac{Σ{x}_{i\left(old\right)}^{2}}{10} - \left(\overset{¯}{x}\left(old\right)\right)^{2}<br/><br />Σ{x}_{i\left(old\right)}^{2} = 1040<br/><br />Σ{x}_{i\left(new\right)}^{2} = 1040 - 64 + 324<br/><br />= 1300<br/>Var(new)=130010−(11)2=130−121=9<br />Var\left(new\right) = \dfrac{1300}{10} - \left(11\right)^{2} = 130 - 121 = 9
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