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In an experiment with 15 observations on x, the following results were available.
∑x2 = 2830, ∑x = 170
One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance was
  • a)
    188.66
  • b)
    177.33
  • c)
    8.33
  • d)
    78.00
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In an experiment with 15 observations on x, the following results wer...
Given data:
- Number of observations (n) = 15
- Sum of squares of x (∑x^2) = 2830
- Sum of x (∑x) = 170

Step 1: Finding the original variance (before replacement)
The variance can be calculated using the formula:
Variance (σ^2) = (∑x^2)/n - (∑x/n)^2

Substituting the given values:
Variance (before replacement) = (2830/15) - (170/15)^2
= 188.66

Step 2: Finding the corrected variance (after replacement)
To find the corrected variance, we need to adjust the sum of squares (∑x^2) and sum of x (∑x) by replacing the wrong value.

- Original sum of squares (∑x^2) = 2830
- Original sum of x (∑x) = 170

After replacing the wrong value (20) with the correct value (30):
- Adjusted sum of squares (∑x^2) = 2830 - 20^2 + 30^2
= 2830 - 400 + 900
= 3330
- Adjusted sum of x (∑x) = 170 - 20 + 30
= 180

The corrected variance can be calculated using the formula:
Corrected Variance (σ^2) = (∑x^2)/n - (∑x/n)^2

Substituting the adjusted values:
Corrected Variance = (3330/15) - (180/15)^2
= 222 - 12^2
= 222 - 144
= 78.00

Conclusion:
After replacing the wrong value with the correct value, the corrected variance is found to be 78.00. Therefore, the correct answer is option D.
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In an experiment with 15 observations on x, the following results were available.∑x2 = 2830, ∑x = 170One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance wasa)188.66b)177.33c)8.33d)78.00Correct answer is option 'D'. Can you explain this answer?
Question Description
In an experiment with 15 observations on x, the following results were available.∑x2 = 2830, ∑x = 170One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance wasa)188.66b)177.33c)8.33d)78.00Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In an experiment with 15 observations on x, the following results were available.∑x2 = 2830, ∑x = 170One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance wasa)188.66b)177.33c)8.33d)78.00Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an experiment with 15 observations on x, the following results were available.∑x2 = 2830, ∑x = 170One observation, which was 20, was found to be wrong and was replaced by the correct value 30. Then, the corrected variance wasa)188.66b)177.33c)8.33d)78.00Correct answer is option 'D'. Can you explain this answer?.
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