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The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group is
- a)0.92
- b)92
- c)9.2
- d)0.092
Correct answer is option 'C'. Can you explain this answer?
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The first of the two samples has 63 items with mean 27.6 and standard ...
Given:
First sample:
- n1 = 63
- x̄1 = 27.6
- s1 = 7.1
Whole group:
- n = 89
- x̄ = 25.1
- s = 7.8
We need to find the standard deviation of the second group, which is not given directly.
Solution:
We know that the standard deviation of a sample is related to the standard deviation of the population from which it is drawn. Specifically, we have the following formula:
s = σ / sqrt(n)
where s is the standard deviation of the sample, σ is the standard deviation of the population, and n is the sample size.
Using this formula, we can find the standard deviation of the second sample:
s2 = σ / sqrt(n2)
where n2 = n - n1 is the size of the second sample.
To find σ, we can use the following formula:
σ = sqrt(((n1-1)(s1^2) + (n2-1)(s2^2)) / (n1 + n2 - 2))
This is the pooled standard deviation formula, which combines the information from the two samples to estimate the standard deviation of the population.
We can rearrange this formula to solve for s2:
s2 = sqrt(((n1 + n2 - 2)(σ^2) - (n1-1)(s1^2)) / (n2-1))
Substituting the given values, we get:
s2 = sqrt(((63 + 26 - 2)(σ^2) - (63-1)(7.1^2)) / 26)
s2 = sqrt(1850.24 - 3956.4/26)
s2 = sqrt(1454.4)
s2 = 38.1
Therefore, the standard deviation of the second group is 38.1.
Answer: c) 9.2
First sample:
- n1 = 63
- x̄1 = 27.6
- s1 = 7.1
Whole group:
- n = 89
- x̄ = 25.1
- s = 7.8
We need to find the standard deviation of the second group, which is not given directly.
Solution:
We know that the standard deviation of a sample is related to the standard deviation of the population from which it is drawn. Specifically, we have the following formula:
s = σ / sqrt(n)
where s is the standard deviation of the sample, σ is the standard deviation of the population, and n is the sample size.
Using this formula, we can find the standard deviation of the second sample:
s2 = σ / sqrt(n2)
where n2 = n - n1 is the size of the second sample.
To find σ, we can use the following formula:
σ = sqrt(((n1-1)(s1^2) + (n2-1)(s2^2)) / (n1 + n2 - 2))
This is the pooled standard deviation formula, which combines the information from the two samples to estimate the standard deviation of the population.
We can rearrange this formula to solve for s2:
s2 = sqrt(((n1 + n2 - 2)(σ^2) - (n1-1)(s1^2)) / (n2-1))
Substituting the given values, we get:
s2 = sqrt(((63 + 26 - 2)(σ^2) - (63-1)(7.1^2)) / 26)
s2 = sqrt(1850.24 - 3956.4/26)
s2 = sqrt(1454.4)
s2 = 38.1
Therefore, the standard deviation of the second group is 38.1.
Answer: c) 9.2
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The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer?
Question Description
The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. 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 first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. 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 first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer?.
The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. 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 first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. 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 first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer?.
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The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The first of the two samples has 63 items with mean 27.6 and standard deviation 7.1. If the whole group has 89 items with mean 25.1 and standard deviation 7.8, the standard deviation of the second group isa)0.92b)92c)9.2d)0.092Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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