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19 May 2023, 22:07
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Difficulty:
55%
(hard)
Question Stats:
62% (01:37) correct
38%
(01:28)
wrong
based on 250
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Set M consists of 100 numbers, with the standard deviation of 10 and the mean of 45. Set N consists of 4 numbers. If all of the numbers in set N are added to set M, will the combined set have a standard deviation greater than 10?
1. The range of set N is 0
2. The sum of the numbers in set N is 180
1. The range of set N is 0
2. The sum of the numbers in set N is 180
23 May 2023, 10:45
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Given information
Set M = no. Of elements = 100
Mean = 45
Standard Deviation = 10
Set N no. Of elements = 4
1) range = 0
We can only infer that standard deviation = 0 . Insufficient
2) sum of set N = 180
Mean = 45
Insufficient
If standard deviation of set N =0 AND MEAN = 45
I.E. all elements are same
If elements of set N are added to the set M . All elements are closer to mean , hence standard deviation will decrease
Hence C is sufficient
Set M = no. Of elements = 100
Mean = 45
Standard Deviation = 10
Set N no. Of elements = 4
1) range = 0
We can only infer that standard deviation = 0 . Insufficient
2) sum of set N = 180
Mean = 45
Insufficient
If standard deviation of set N =0 AND MEAN = 45
I.E. all elements are same
If elements of set N are added to the set M . All elements are closer to mean , hence standard deviation will decrease
Hence C is sufficient
05 Sep 2024, 11:27
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This is more of inference type of question.
Here M consists of 100 numbers with std dev = 10 and mean 45
now set N which consists of 4 numbers are added to M. how it will affect the std dev of entire combined set
case 1 : All 4 numbers of N are equally distributed from mean M on either side such that their total is zero. then there won't be any change in std. dev.
case 2 : if all numbers from N are greater than mean or their resultant is more than 45 then std dev will go up (>10)
case 3 : if all numbers from N are less than mean or their resultant is less than 45 then std dev will go down (<10)
Statement 1 : The sum of numbers from N is 180. Well we have many possibilities to distribute 180 in 4 nos. Nothing specific can be inferred
combine 1 and 2 : sum is 180 and all are same. Then each number is 45. That means std dev remain same
which answers our yes/no type question
hence C
Range of N is zero that means all elements of N are essentially same. But are they equal to 45 (in such case std dev will be unchanged). are they more than 45 (then SD >10) or are they less than 45 (then SD < 10).
we can't infer anything
Statement 2 :
Here M consists of 100 numbers with std dev = 10 and mean 45
now set N which consists of 4 numbers are added to M. how it will affect the std dev of entire combined set
case 1 : All 4 numbers of N are equally distributed from mean M on either side such that their total is zero. then there won't be any change in std. dev.
case 2 : if all numbers from N are greater than mean or their resultant is more than 45 then std dev will go up (>10)
case 3 : if all numbers from N are less than mean or their resultant is less than 45 then std dev will go down (<10)
Statement 1 : The sum of numbers from N is 180. Well we have many possibilities to distribute 180 in 4 nos. Nothing specific can be inferred
combine 1 and 2 : sum is 180 and all are same. Then each number is 45. That means std dev remain same
which answers our yes/no type question
hence C
Range of N is zero that means all elements of N are essentially same. But are they equal to 45 (in such case std dev will be unchanged). are they more than 45 (then SD >10) or are they less than 45 (then SD < 10).
we can't infer anything
Statement 2 :
