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A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ?
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A student obtained the mean and standard deviation of 100 observation ...
Calculating the Correct Mean:
To calculate the correct standard deviation, we first need to recalculate the mean by removing the wrongly copied observation and replacing it with the correct value. The correct mean can be calculated as follows:
Correct Mean = ((Sum of all observations) - (Wrongly copied observation) + (Correct observation)) / (Total number of observations)
The sum of all observations can be calculated as 40 * 100 = 4000. Therefore,
Correct Mean = ((4000) - (50) + (40)) / (100) = 39.9
Therefore, the correct mean is 39.9.
Calculating the Correct Standard Deviation:
To calculate the correct standard deviation, we can use the formula:
Correct Standard Deviation = Square Root of (((Sum of (each observation - mean)^2) - (Wrongly copied observation - mean)^2 + (Correct observation - mean)^2) / (Total number of observations))
The sum of (each observation - mean)^2 can be calculated as follows:
(40 - 39.9)^2 + (40 - 39.9)^2 + … + (50 - 39.9)^2 + … + (40 - 39.9)^2
= (0.1)^2 + (0.1)^2 + … + (10.1)^2 + … + (0.1)^2
= 5.1^2 * 100 = 26010
The wrongly copied observation is 50, which should have been 40. Therefore, the (Wrongly copied observation - mean)^2 is:
(50 - 40)^2 = 100
The correct observation is 40, and the correct mean is 39.9. Therefore, the (Correct observation - mean)^2 is:
(40 - 39.9)^2 = 0.01
Therefore, the correct standard deviation is:
Correct Standard Deviation = Square Root of (((Sum of (each observation - mean)^2) - (Wrongly copied observation - mean)^2 + (Correct observation - mean)^2) / (Total number of observations))
= Square Root of ((26010 - 100 + 0.01) / 100)
= Square Root of (25910.01 / 100)
= Square Root of 259.1001
= 16.096
Therefore, the correct standard deviation is 16.096.
Explanation:
The correct mean is slightly lower than the original mean of 40, which is expected since the wrongly copied observation was higher than the actual value. The correct standard deviation is significantly higher than the original standard deviation of 5.1, which is also expected since the wrongly copied observation was an outlier that skewed the original standard deviation. By removing the outlier and recalculating the mean and standard deviation, we get a more accurate representation of the data.
To calculate the correct standard deviation, we first need to recalculate the mean by removing the wrongly copied observation and replacing it with the correct value. The correct mean can be calculated as follows:
Correct Mean = ((Sum of all observations) - (Wrongly copied observation) + (Correct observation)) / (Total number of observations)
The sum of all observations can be calculated as 40 * 100 = 4000. Therefore,
Correct Mean = ((4000) - (50) + (40)) / (100) = 39.9
Therefore, the correct mean is 39.9.
Calculating the Correct Standard Deviation:
To calculate the correct standard deviation, we can use the formula:
Correct Standard Deviation = Square Root of (((Sum of (each observation - mean)^2) - (Wrongly copied observation - mean)^2 + (Correct observation - mean)^2) / (Total number of observations))
The sum of (each observation - mean)^2 can be calculated as follows:
(40 - 39.9)^2 + (40 - 39.9)^2 + … + (50 - 39.9)^2 + … + (40 - 39.9)^2
= (0.1)^2 + (0.1)^2 + … + (10.1)^2 + … + (0.1)^2
= 5.1^2 * 100 = 26010
The wrongly copied observation is 50, which should have been 40. Therefore, the (Wrongly copied observation - mean)^2 is:
(50 - 40)^2 = 100
The correct observation is 40, and the correct mean is 39.9. Therefore, the (Correct observation - mean)^2 is:
(40 - 39.9)^2 = 0.01
Therefore, the correct standard deviation is:
Correct Standard Deviation = Square Root of (((Sum of (each observation - mean)^2) - (Wrongly copied observation - mean)^2 + (Correct observation - mean)^2) / (Total number of observations))
= Square Root of ((26010 - 100 + 0.01) / 100)
= Square Root of (25910.01 / 100)
= Square Root of 259.1001
= 16.096
Therefore, the correct standard deviation is 16.096.
Explanation:
The correct mean is slightly lower than the original mean of 40, which is expected since the wrongly copied observation was higher than the actual value. The correct standard deviation is significantly higher than the original standard deviation of 5.1, which is also expected since the wrongly copied observation was an outlier that skewed the original standard deviation. By removing the outlier and recalculating the mean and standard deviation, we get a more accurate representation of the data.
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A student obtained the mean and standard deviation of 100 observation ...
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A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ?
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A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ? 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 A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ?.
A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ? 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 A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student obtained the mean and standard deviation of 100 observation as 40 and 5.1 respectively. It was later discovered that he had wrongly copied down an observation as 50 instead of 40. The correct standard deviation is ?.
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