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29 May 2020, 17:40
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C
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Difficulty:
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70% (00:42) correct
30%
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based on 66
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what is the standard deviation of M?
(1) Set M contains 17 terms.
(2) M is a set of consecutive integers
(1) Set M contains 17 terms.
(2) M is a set of consecutive integers
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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29 May 2020, 20:15
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Even if you do not know the formula of Standard Deviation, for solving SD questions, you only need to know two inputs -
1. the # of values in the set
2. relative position of values in the set. i.e. if they are consecutive, evenly spaced, unevenly spaced, etc.
(That's because SD shows how much variation there is from the mean)
Additionally, two very important properties of standard deviation:
(a) If we add or subtract a constant to each term in a set -
Mean will increase or decrease by the same constant.
SD will not change.
(b) If we multiply all terms by a constant (the same percent ) -
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
Coming to the question at hand -
Option (1) Set M contains 17 terms.
Satisfies input 1. but not 2. (mentioned at top of the post)
For example: M could be first 17 consecutive positive numbers i.e. (1, 2, 3, ... 17)
M could also be a set of 17 odd numbers starting 1 i.e. (1, 3, 5, ... 33)
Here, the mean of both the above sets (and the relative distance of each number from the mean) is different. Hence, the SD will be different.
Not Sufficient
Option (2) M is a set of consecutive integer.s
Satisfies input 2. but not 1. (mentioned at top of the post)
For example: M could be first 10 consecutive positive numbers i.e. (1, 2, 3, ... 10)
M could also be a set of 3 consecutive numbers starting 5 i.e. (5, 6, 7)
Here, as the number of vales in each set will be different, the mean of both the above sets is different. Thus, the SD will be different.
Not Sufficient
Combining Option (1) and Option (2)
Now we know there are 17 vales in the set. Additionally, we know that these 17 values are consecutive.
Satisfies both input 1. & 2. (as mentioned at the top of this post)
This set could be any 17 consecutive values. Consider property (a) mentioned at the start of this post - SD will not change if a constant is added or subtracted from each term of the series.
Hence, we know the difference between the mean and each number will be 1,2,3,4,5,6,7,8,0,8,7,6,5,4,3,2,1 no matter what the mean is, so you can calculate SD from this.
Sufficient
Answer is C
1. the # of values in the set
2. relative position of values in the set. i.e. if they are consecutive, evenly spaced, unevenly spaced, etc.
(That's because SD shows how much variation there is from the mean)
Additionally, two very important properties of standard deviation:
(a) If we add or subtract a constant to each term in a set -
Mean will increase or decrease by the same constant.
SD will not change.
(b) If we multiply all terms by a constant (the same percent ) -
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
Coming to the question at hand -
Option (1) Set M contains 17 terms.
Satisfies input 1. but not 2. (mentioned at top of the post)
For example: M could be first 17 consecutive positive numbers i.e. (1, 2, 3, ... 17)
M could also be a set of 17 odd numbers starting 1 i.e. (1, 3, 5, ... 33)
Here, the mean of both the above sets (and the relative distance of each number from the mean) is different. Hence, the SD will be different.
Not Sufficient
Option (2) M is a set of consecutive integer.s
Satisfies input 2. but not 1. (mentioned at top of the post)
For example: M could be first 10 consecutive positive numbers i.e. (1, 2, 3, ... 10)
M could also be a set of 3 consecutive numbers starting 5 i.e. (5, 6, 7)
Here, as the number of vales in each set will be different, the mean of both the above sets is different. Thus, the SD will be different.
Not Sufficient
Combining Option (1) and Option (2)
Now we know there are 17 vales in the set. Additionally, we know that these 17 values are consecutive.
Satisfies both input 1. & 2. (as mentioned at the top of this post)
This set could be any 17 consecutive values. Consider property (a) mentioned at the start of this post - SD will not change if a constant is added or subtracted from each term of the series.
Hence, we know the difference between the mean and each number will be 1,2,3,4,5,6,7,8,0,8,7,6,5,4,3,2,1 no matter what the mean is, so you can calculate SD from this.
Sufficient
Answer is C
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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