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20 Jul 2020, 02:56
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
39% (01:31) correct
61%
(01:33)
wrong
based on 292
sessions
History
Date
Time
Result
Not Attempted Yet
A zoologist recorded the number of cubs under the care of each of 12 adult female lions. What was the standard deviation of the numbers of cubs under the care of the 12 adult female lions?
(1) Each of the 12 adult female lions had either 2 or 3 cubs under her care.
(2) 8 of the 12 adult female lions had the same number of cubs under her care.
Are You Up For the Challenge: 700 Level Questions
(1) Each of the 12 adult female lions had either 2 or 3 cubs under her care.
(2) 8 of the 12 adult female lions had the same number of cubs under her care.
Are You Up For the Challenge: 700 Level Questions
20 Jul 2020, 09:46
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The answer here is C, not E. Using both statements, we only have two possible lists, since every value is either 2 or 3, and we know we have eight of one number and four of the other. So we have one of these two lists:
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3
2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3
The standard deviation of these two lists is the same, because the distances separating the values is the same in each (one list is just the "mirror image" of the other). If it's not clear why that should mean the two lists have identical standard deviations, you could find the mean of each list (it's 8/3 in the first list, 7/3 in the second), and then find the distance from each value to the mean. In each, you'll find that four of the distances are 1/3, and eight are 2/3, so for either list you'd feed the same list of distances into the standard deviation calculation, and therefore get the same answer either way.
2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3
2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3
The standard deviation of these two lists is the same, because the distances separating the values is the same in each (one list is just the "mirror image" of the other). If it's not clear why that should mean the two lists have identical standard deviations, you could find the mean of each list (it's 8/3 in the first list, 7/3 in the second), and then find the distance from each value to the mean. In each, you'll find that four of the distances are 1/3, and eight are 2/3, so for either list you'd feed the same list of distances into the standard deviation calculation, and therefore get the same answer either way.
General Discussion
Updated on: 21 Jul 2020, 03:17
Originally posted by Varunsawhney8 on 20 Jul 2020, 03:31.
Last edited by Varunsawhney8 on 21 Jul 2020, 03:17, edited 1 time in total.
Last edited by Varunsawhney8 on 21 Jul 2020, 03:17, edited 1 time in total.
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Answer should be c
Statement 1-
Not Sufficient
(many possibilities)
Statement 2-
Let each of 8 female Lions has a cubs
and each of 4 female lions has b cubs
Total cubs= 8a+4b
Will not get any information further from this (many possibilities)
Statement 1 and 2 together
values of (a,b) can be (3,2) or (2,3)
Selecting (a,b) 3,2
I.e. 8 number have 3 cubs
And 4 number have 2 cubs each
Mean- 32/12= 2.66
Standard deviation=√(x-mean)^2/n
Difference of mean and values
8 values- 0.33, 4 values- 0.66
Selecting (a,b) 3,2
I.e. 8 number have 3 cubs
And 4 number have 2 cubs each
Mean- 28/12=2.33
Standard deviation=√(x-mean)^2/n
Difference of mean and values
8 values- 0.33, 4 values- 0.66
So we will get same answer.
sufficient
Statement 1-
Not Sufficient
(many possibilities)
Statement 2-
Let each of 8 female Lions has a cubs
and each of 4 female lions has b cubs
Total cubs= 8a+4b
Will not get any information further from this (many possibilities)
Statement 1 and 2 together
values of (a,b) can be (3,2) or (2,3)
Selecting (a,b) 3,2
I.e. 8 number have 3 cubs
And 4 number have 2 cubs each
Mean- 32/12= 2.66
Standard deviation=√(x-mean)^2/n
Difference of mean and values
8 values- 0.33, 4 values- 0.66
Selecting (a,b) 3,2
I.e. 8 number have 3 cubs
And 4 number have 2 cubs each
Mean- 28/12=2.33
Standard deviation=√(x-mean)^2/n
Difference of mean and values
8 values- 0.33, 4 values- 0.66
So we will get same answer.
sufficient
Bunuel
