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The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denote
the distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?
the distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?
- a)Standard Deviation (P) = Standard Deviation (Q)
- b)Standard Deviation (P) = - Standard Deviation (Q)
- c)Standard Deviation (P) = Standard Deviation (Q) + 2
- d)Standard Deviation (P) = 2* Standard Deviation (Q)
- e)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The numbers in set P denote the distance of certain positive integers ...
Given:
- Let the integers be a, b, c, d, e….
- Set P = {Respective Distance of a, b, c, , d, e…. from -1}
- Set Q = {Respective Distance of a, b, c, d, e…from 1}
To Find: the statement, which is true about the standard deviation of sets P and Q
Approach:
- To find the relation between the standard deviation of sets P and Q, we would need to find the relation between the terms that are present in sets P and Q
- Terms in set P
- We know that distance of a number x from -1 on the number line can be written as |x –(-1)| = |x +1|
- We will use the above understanding to write down the terms of set P
- Terms in set Q
- We know that distance of a number x from 1 on the number line can be written as |x -1|
- We will use the above understanding to write down the terms of set Q
- Once we write down the terms of sets P and Q, we will find the relation between the terms of these 2 sets. Then, we'll use the standard properties of standard deviation to compare the standard deviation of sets P and Q.
Working out:
- Terms in set P
- Set P = {|a+1|, |b+1|, |c+1|…….}
- Terms in set Q
- Set Q = {|a-1|, |b-1|, |c-1|…….} = {|(a + 1) -2|, |(b+1) -2|, |(c+1) -2|……..}
- We can observe that if we subtract 2 from each of the terms of set P, we will get the terms of set Q.
- We know from the property of standard deviation that reducing all the terms of a set by the same constant does not change the standard deviation of the set.
- So, we can write Standard Deviation(P) = Standard Deviation(Q)
Answer : A
Most Upvoted Answer
The numbers in set P denote the distance of certain positive integers ...
Explanation:
- The formula for standard deviation is the square root of the variance.
- The variance is the average of the squared differences from the mean.
- For set P, the mean is (distance from -1 + distance from 1)/2 = distance from 0.
- For set Q, the mean is (distance from 1 + distance from -1)/2 = distance from 0.
- Since both sets have the same mean, the variance will be the same as well.
- Therefore, the standard deviation of set P is equal to the standard deviation of set Q.
- Hence, the correct option is (a) Standard Deviation (P) = Standard Deviation (Q).
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The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The numbers in set P denote the distance of certain positive integers from -1 on the number line. The numbers in set Q denotethe distance of the same integers from 1 on the number line. Which of the following statements is true about the standard deviation of the sets P and Q?a)Standard Deviation (P) = Standard Deviation (Q)b)Standard Deviation (P) = - Standard Deviation (Q)c)Standard Deviation (P) = Standard Deviation (Q) + 2d)Standard Deviation (P) = 2* Standard Deviation (Q)e)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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