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

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

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

STANDARD DEVIATION = How scattered are the numbers away from its mean.
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

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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