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

NTA Abhyas 2020 · Mathematics · Statistics

In an experiment with 9 observations on x , the following results...

In an experiment with 99 observations on xx, the following results are available ∑x2=360and∑x=34∑ x^{2} = 360 and ∑ x = 34. One observation that was 8,8, was found to be wrong and was replaced by the correct value 10,10, then the corrected variance is

Options

  1. A2509\dfrac{250}{9}
  2. B2828
  3. C2409\dfrac{240}{9}
  4. D2828

Correct answer

B. 2828

Step-by-step solution

∑x2=360,∑x=34∑ x^{2} = 360, ∑ x = 34
corrected∑x′=34–8+10=36∑ x^{'} = 34 – 8 + 10 = 36
corrected ∑x′2=360+100–64=396∑ x^{'2} = 360 + 100 – 64 = 396
The corrected variance =∑x′29–(∑x9)2=3969–(369)2= \dfrac{∑ x^{'2}}{9} – {\left(\dfrac{∑ x}{9}\right)}^{2} = \dfrac{396}{9} – {\left(\dfrac{36}{9}\right)}^{2}
=44–16=28= 44 – 16 = 28
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