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The standard deviation of the weights (in kg) of the students of a class of 50 students was calculated to be 4.5 kg. Later on it was found that due to some fault in weighing machine, the weight of each student was under measured by 0.5 kg. The Correct standard deviation of the weight will be:
- a)Less than 4.5
- b)Greater than 4.5
- c)Equal to 4.5
- d)Can not be determined
Correct answer is option 'C'. Can you explain this answer?
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The standard deviation of the weights (in kg) of the students of a cla...
Given information:
- Standard deviation of weights of 50 students = 4.5 kg
- Each student's weight was under measured by 0.5 kg
To find: Correct standard deviation of the weight
Effect of under measurement on mean and standard deviation:
- Mean is shifted by the same amount as the under measurement
- Standard deviation remains the same
Therefore, the correct standard deviation of the weight will be equal to the original standard deviation of 4.5 kg.
Explanation:
- The standard deviation is a measure of the spread of data around the mean.
- It is calculated using the formula: σ = √(Σ(xi - μ)²/n), where σ is the standard deviation, xi is the individual data point, μ is the mean, and n is the sample size.
- In this case, the standard deviation of the weights of 50 students was calculated to be 4.5 kg.
- Later on, it was found that the weight of each student was under measured by 0.5 kg. This means that the actual weight of each student is 0.5 kg more than what was measured.
- However, this under measurement affects only the mean of the data, and not the standard deviation.
- The correct mean of the data will be shifted by 0.5 kg, but the spread of the data around the mean will remain the same.
- Therefore, the correct standard deviation of the weight will be the same as the original standard deviation of 4.5 kg.
- Hence, the correct answer is option 'C': Equal to 4.5.
- Standard deviation of weights of 50 students = 4.5 kg
- Each student's weight was under measured by 0.5 kg
To find: Correct standard deviation of the weight
Effect of under measurement on mean and standard deviation:
- Mean is shifted by the same amount as the under measurement
- Standard deviation remains the same
Therefore, the correct standard deviation of the weight will be equal to the original standard deviation of 4.5 kg.
Explanation:
- The standard deviation is a measure of the spread of data around the mean.
- It is calculated using the formula: σ = √(Σ(xi - μ)²/n), where σ is the standard deviation, xi is the individual data point, μ is the mean, and n is the sample size.
- In this case, the standard deviation of the weights of 50 students was calculated to be 4.5 kg.
- Later on, it was found that the weight of each student was under measured by 0.5 kg. This means that the actual weight of each student is 0.5 kg more than what was measured.
- However, this under measurement affects only the mean of the data, and not the standard deviation.
- The correct mean of the data will be shifted by 0.5 kg, but the spread of the data around the mean will remain the same.
- Therefore, the correct standard deviation of the weight will be the same as the original standard deviation of 4.5 kg.
- Hence, the correct answer is option 'C': Equal to 4.5.
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Community Answer
The standard deviation of the weights (in kg) of the students of a cla...
Standard deviation is affected by shift of scale but not by shift of origin. So, the value remains the same.
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The standard deviation of the weights (in kg) of the students of a class of 50 students was calculated to be 4.5 kg. Later on it was found that due to some fault in weighing machine, the weight of each student was under measured by 0.5 kg. The Correct standard deviation of the weight will be:a)Less than 4.5b)Greater than 4.5c)Equal to 4.5d)Can not be determinedCorrect answer is option 'C'. Can you explain this answer?
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