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NTA Abhyas JEE Main2020MathematicsStatisticsPractice

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 , respectively by a student who took by mistake 50 instead of 40 for one observation, then the correct standard deviation is

Options

  1. A4
  2. B6
  3. C3
  4. D5

Correct answer

D. 5

Step-by-step solution

Standard deviation σ = 1 n ∑ i = 1 n x i 2 - 1 n 2 ∑ i = 1 n x i 2 = 1 n ∑ i = 1 n x i 2 - x - 2 ⇒ 5.1 = 1 100 × I n c o r r e c t ∑ i = 1 n x i 2 - 40 2 or, 26.01 = 1 100 × Incorrect ∑ i = 1 n x i 2 - 1600 Therefore, Incorrect ∑ i = 1 n x i 2 = 100 ( 26 .01 + 1600 ) = 162601 Correct mean, x   ¯ = 3990 100 = 39 . 9 Now, Correct ∑ i = 1 n x i 2 = Incorrect ∑ i = 1 n x i 2 - 50 2 + 40 2 = 162601 - 2500 + 1600 = 161701 Therefore correct sta

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