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The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?
- a)45, 5
- b)11.25, 1.25
- c)11.25, 2.5
- d)12.5, 2.5
Correct answer is option 'C'. Can you explain this answer?
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The mean of 100 observations is 50 and the standard deviation is 10. I...
Now the new standard deviation 
[As addition and subtraction does not affect σ].
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The mean of 100 observations is 50 and the standard deviation is 10. I...
New Mean Calculation:
To find the new mean, we need to subtract 5 from each observation and then divide by 4. Let's denote the original observations as X and the new observations as Y. The relationship between X and Y can be expressed as:
Y = (X - 5) / 4
By substituting the original mean into this equation, we can find the new mean:
New Mean = (Mean - 5) / 4
New Mean = (50 - 5) / 4 = 45 / 4 = 11.25
Therefore, the new mean is 11.25.
New Standard Deviation Calculation:
To find the new standard deviation, we need to consider the effect of subtracting 5 and dividing by 4 on the spread of the data. Let's denote the original standard deviation as σX and the new standard deviation as σY. The relationship between σX and σY can be expressed as:
σY = σX / 4
In other words, dividing each observation by 4 reduces the standard deviation by a factor of 4. Therefore, the new standard deviation will be:
New Standard Deviation = Standard Deviation / 4
New Standard Deviation = 10 / 4 = 2.5
Therefore, the new standard deviation is 2.5.
Conclusion:
The new mean after subtracting 5 from each observation and then dividing by 4 is 11.25, and the new standard deviation is 2.5. Therefore, the correct answer is option C) 11.25, 2.5.
To find the new mean, we need to subtract 5 from each observation and then divide by 4. Let's denote the original observations as X and the new observations as Y. The relationship between X and Y can be expressed as:
Y = (X - 5) / 4
By substituting the original mean into this equation, we can find the new mean:
New Mean = (Mean - 5) / 4
New Mean = (50 - 5) / 4 = 45 / 4 = 11.25
Therefore, the new mean is 11.25.
New Standard Deviation Calculation:
To find the new standard deviation, we need to consider the effect of subtracting 5 and dividing by 4 on the spread of the data. Let's denote the original standard deviation as σX and the new standard deviation as σY. The relationship between σX and σY can be expressed as:
σY = σX / 4
In other words, dividing each observation by 4 reduces the standard deviation by a factor of 4. Therefore, the new standard deviation will be:
New Standard Deviation = Standard Deviation / 4
New Standard Deviation = 10 / 4 = 2.5
Therefore, the new standard deviation is 2.5.
Conclusion:
The new mean after subtracting 5 from each observation and then dividing by 4 is 11.25, and the new standard deviation is 2.5. Therefore, the correct answer is option C) 11.25, 2.5.
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The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer?
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The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer?.
The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean of 100 observations is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard deviation respectively?a)45, 5b)11.25, 1.25c)11.25, 2.5d)12.5, 2.5Correct answer is option 'C'. Can you explain this answer?.
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