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The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is:
- a)2
- b)4
- c)0
- d)1
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The mean and the standard deviation (s.d.) of five observations are 9 ...
Here mean = 
Now, standard deviation = 0
∴ all the five terms are same i.e., 9.
Now for changed observation
= 2
Now, standard deviation = 0
∴ all the five terms are same i.e., 9.
Now for changed observation
= 2
Most Upvoted Answer
The mean and the standard deviation (s.d.) of five observations are 9 ...
Given:
Mean = 9
Standard Deviation = 0
To Find:
Standard Deviation of the new set of observations
Solution:
Let's assume the five observations as x1, x2, x3, x4, and x5.
Step 1:
We are given that the mean of the five observations is 9.
Therefore, we can write the equation:
(x1 + x2 + x3 + x4 + x5) / 5 = 9
Step 2:
We are given that the standard deviation of the five observations is 0.
Therefore, we can write the equation:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Step 3:
Now, let's assume one of the observations, let's say x1, is changed and the mean of the new set becomes 10.
Therefore, we can write the equation:
(x1 + x2 + x3 + x4 + x5) / 5 = 10
Step 4:
We need to find the new standard deviation.
Let's assume the new standard deviation as s.
Step 5:
Using the equation from Step 2, we can rewrite it as:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Now, substituting the equation from Step 3, we get:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
[(x1 - 10 + 1)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
[(x1 - 10)^2 + 1 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Step 6:
Simplifying the equation, we get:
[(x1 - 10)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = -1
Since the numerator of the equation represents the sum of squares, it cannot be negative.
Therefore, the equation is not possible.
Conclusion:
Hence, the new set of observations cannot have a standard deviation other than 0.
Therefore, the correct answer is option 'C' - 0.
Mean = 9
Standard Deviation = 0
To Find:
Standard Deviation of the new set of observations
Solution:
Let's assume the five observations as x1, x2, x3, x4, and x5.
Step 1:
We are given that the mean of the five observations is 9.
Therefore, we can write the equation:
(x1 + x2 + x3 + x4 + x5) / 5 = 9
Step 2:
We are given that the standard deviation of the five observations is 0.
Therefore, we can write the equation:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Step 3:
Now, let's assume one of the observations, let's say x1, is changed and the mean of the new set becomes 10.
Therefore, we can write the equation:
(x1 + x2 + x3 + x4 + x5) / 5 = 10
Step 4:
We need to find the new standard deviation.
Let's assume the new standard deviation as s.
Step 5:
Using the equation from Step 2, we can rewrite it as:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Now, substituting the equation from Step 3, we get:
[(x1 - 9)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
[(x1 - 10 + 1)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
[(x1 - 10)^2 + 1 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = 0
Step 6:
Simplifying the equation, we get:
[(x1 - 10)^2 + (x2 - 9)^2 + (x3 - 9)^2 + (x4 - 9)^2 + (x5 - 9)^2] / 5 = -1
Since the numerator of the equation represents the sum of squares, it cannot be negative.
Therefore, the equation is not possible.
Conclusion:
Hence, the new set of observations cannot have a standard deviation other than 0.
Therefore, the correct answer is option 'C' - 0.
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The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is:a)2b)4c)0d)1Correct answer is option 'A'. Can you explain this answer?
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The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is:a)2b)4c)0d)1Correct answer is option 'A'. 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 The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is:a)2b)4c)0d)1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is:a)2b)4c)0d)1Correct answer is option 'A'. Can you explain this answer?.
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