A zoologist recorded the number of cubs under the care of each of 12 a

Question

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.

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Varunsawhney8 · Answer

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

RaghavKhanna · Answer

St 1:  
The number of cubs with each adult female lions is 2 or 3.
=> Many possibilities for the total number of cubs
=> Many possible values for standard deviation

=>  St. 1 is insufficient

St 2:  
8 of the 12 female lions have the same number of cubs.
=> Number of cubs of 8 female lions = 8x

But no information about the number of cubs with other female lions.
=> Cannot calculate the total number of cubs

=>  St. 2 is insufficient

St. 1 & St. 2: 
No additional information to find the number of cubs.
=>  St. 1 & St. 2 together are insufficient

Answer: E

IanStewart · Answer

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.

p05eidon · Answer

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?

Statement - 1 
(1) Each of the 12 adult female lions had either 2 or 3 cubs under her care.

Doesn't really help us in finding the SD as there would be many possible combinations.
So, Statement A is insufficient.

Statement-2 
(2) 8 of the 12 adult female lions had the same number of cubs under her care.

If we don't know how many cubs each lion is having, we cannot find the mean.
If we cannot find the mean, we cannot find the SD.

Combining Statement 1 and 2

if we combine, there would still be 2 possibilities, i.e. 
8 lions with 2 cubs, 4 with 3 cubs or 
8 lions with 3 cubs and 4 with 2 cubs.
In both cases, the resulting SD is the same.
So combining these is sufficient.

Option C

Merc · Answer

NOTE : GMAT never requires us to calculate the standard deviation , it is all logic ,
This is anyway a DS question , no need to calculate , here is how.

STEM- 12 adult lions have curbs under each of them .

STAT 1 - it says either 2 or 3,
BUT if all are 2 then SD is zero , if some are 2 while some are 3 , then its 1
NOT SUFF.

STAT 2- 8/12 have same number of curbs , what about other 4 ?
They could be any number .
NOT SUFF

COMBINING 1 & 2 - number of curbs is either 2 or 3 .. & we know that 8/12 have the same number
that means it could be 2,2,2,2,2,2,2,2,3,3,3,3 or 3,3,3,3,3,3,3,3,2,2,2,2
IF you look at the both these cases the numbers scattered away from the mean is symmetrical , Hence standard deviation in both the cases is the same.
ANSWER C

THANKYOU
MERC

TestPrepUnlimited · Answer

We want to know the standard deviation of 12 values. Since the question does not mention any other standard deviation values for reference, we will have to calculate this standard deviation from scratch. This means we would like to know these 12 values exactly.

Statement 1:

Our set of 12 values is adjustable so the standard deviation can vary. Insufficient.

Statement 2:

Our set of 12 values is adjustable so the standard deviation can vary. Insufficient.

Combined:

We either have 8 two's and 4 three's, or 8 three's and 4 two's.  We can note these are reverse sets because the spread between values is the same, one set has the spread in the opposite direction but this means their relative distance is exactly the same, hence they have the same standard deviations.   There is only one value for std so combined sufficient.

There is a fast way to check they have the same standard deviation, instead of using 12 values we can reduce the sets down to 3 values, either (2, 2, 3) or (2, 3, 3) will be our viable sets. Subtract the mean from each set, then we are dealing with (-1/3, -1/3, 2/3) and (-2/3, 1/3, 1/3). As we can see the standard deviation would be the same.

Hence set's like (1, 1, 1, 5) and (5, 5, 5, 1) would have the same standard deviation.

Ans: C

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A zoologist recorded the number of cubs under the care of each of 12 a

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A zoologist recorded the number of cubs under the care of each of 12 a

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