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The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would be
- a)4.90
- b)5.00
- c)4.88
- d)4.85
Correct answer is option 'B'. Can you explain this answer?
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The mean and SD of a sample of 100 observations were calculated as 40 ...
Calculating the Correct Mean
To calculate the correct mean after the mistake, we need to subtract the incorrect observation and add the correct observation.
- Sum of original observations = 100 x 40 = 4000
- Correct sum of observations = 4000 - 50 + 40 = 3990
- Correct mean = 3990/100 = 39.9
Calculating the Correct Standard Deviation
To calculate the correct standard deviation after the mistake, we need to use the formula for sample standard deviation with n-1 degrees of freedom.
- Original sum of squares = ∑(x-40)² = 100 x 5.1² = 2601
- Incorrect sum of squares = 2601 + (50-40)² - (40-40)² = 2651
- Correct sum of squares = 2651 - (50-39.9)² + (40-39.9)² = 2611.29
- Correct sample standard deviation = √(2611.29/99) = 5.00
Therefore, the current value of SD would be 5.00 (option B).
To calculate the correct mean after the mistake, we need to subtract the incorrect observation and add the correct observation.
- Sum of original observations = 100 x 40 = 4000
- Correct sum of observations = 4000 - 50 + 40 = 3990
- Correct mean = 3990/100 = 39.9
Calculating the Correct Standard Deviation
To calculate the correct standard deviation after the mistake, we need to use the formula for sample standard deviation with n-1 degrees of freedom.
- Original sum of squares = ∑(x-40)² = 100 x 5.1² = 2601
- Incorrect sum of squares = 2601 + (50-40)² - (40-40)² = 2651
- Correct sum of squares = 2651 - (50-39.9)² + (40-39.9)² = 2611.29
- Correct sample standard deviation = √(2611.29/99) = 5.00
Therefore, the current value of SD would be 5.00 (option B).
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The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would bea)4.90b)5.00c)4.88d)4.85Correct answer is option 'B'. Can you explain this answer?
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The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would bea)4.90b)5.00c)4.88d)4.85Correct answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would bea)4.90b)5.00c)4.88d)4.85Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and SD of a sample of 100 observations were calculated as 40 and 5.1 respectively by a CA student who took one observation as 50 instead of 40 by mistake. The current value of SD would bea)4.90b)5.00c)4.88d)4.85Correct answer is option 'B'. Can you explain this answer?.
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