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06 Jan 2020, 01:03
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B
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Difficulty:
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Question Stats:
65% (01:11) correct
35%
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wrong
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What is the standard deviation of the set {a, b, c, d, e}?
1) The ratio a:b:c:d:e is 1:2:3:4:5.
2) a, b, c, d, and e are consecutive even integers.
1) The ratio a:b:c:d:e is 1:2:3:4:5.
2) a, b, c, d, and e are consecutive even integers.
06 Jan 2020, 04:13
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To find the Standard Deviation we need to find how far the numbers are from each other. There are two theories involved in this question:
1. If all the numbers in the set are increased/decreased by the same number(k) then the Standard Deviation and the Variance DO NOT CHANGE!
2. If all the numbers in the set are multiplied/divided by the same number(k) then the Standard Deviation also gets multiplied by the same number!
You Can find more detailed post on How to Solve Statistics
STAT 1: Since the ratios of the numbers are given so (2.) above is applicable. Since we do not know the exact values of the numbers so the standard deviation can be anything. Example 1,2,3,4,5 set will have a different standard deviation and 2,4,6,8,10 will have a different standard deviation.
So, NOT SUFFICIENT
STAT2: Since a,b,c,d,e are consecutive even numbers so we know that from the mean the numbers are -4,-2,0,2,4 away, which is sufficient to solve for standard deviation. Example: 2,4,6,8,10 will have the same standard deviation as 4,6,8,10,12 because as compared to the mean the values are spread in the same way.
So, Stat 2 is SUFFICIENT.
So, answer will be B
Hope it helps!
1. If all the numbers in the set are increased/decreased by the same number(k) then the Standard Deviation and the Variance DO NOT CHANGE!
2. If all the numbers in the set are multiplied/divided by the same number(k) then the Standard Deviation also gets multiplied by the same number!
You Can find more detailed post on How to Solve Statistics
STAT 1: Since the ratios of the numbers are given so (2.) above is applicable. Since we do not know the exact values of the numbers so the standard deviation can be anything. Example 1,2,3,4,5 set will have a different standard deviation and 2,4,6,8,10 will have a different standard deviation.
So, NOT SUFFICIENT
STAT2: Since a,b,c,d,e are consecutive even numbers so we know that from the mean the numbers are -4,-2,0,2,4 away, which is sufficient to solve for standard deviation. Example: 2,4,6,8,10 will have the same standard deviation as 4,6,8,10,12 because as compared to the mean the values are spread in the same way.
So, Stat 2 is SUFFICIENT.
So, answer will be B
Hope it helps!
18 Aug 2023, 02:07
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CAMANISHPARMAR
Solution:
Pre Analysis:
- We are asked the SD of set {a, b, c, d, e}
- We have to keep in mind that SD is the measure of how spread apart the data is in a set
Statement 1: The ratio \(a:b:c:d:e\) is \(1:2:3:4:5\)
- Ratio does not tell us how far apart the data is
- Let is take 2 sets with ratio \(1:2:3:4:5\)
- SD of {2, 4, 6, 8, 10} will be less than SD of {6, 12, 18, 24, 30}
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: a, b, c, d, and e are consecutive even integers
- So, the set becomes \(2n, 2n+2, 2n+4, 2n+6, 2n+8\)
- Every such set will be equally spread apart
- Be it {2, 4, 6, 8, 10} or {100, 102, 104, 106, 108} both will have same SD which we can calculate if needed
- Thus, statement 2 alone is sufficient
Hence the right answer is Option B
