A local municipality did a census of earthworms per acre of soil for 1

Statement 1: By the end of the year, the range of the number of worms per acre for the sites had increased by 20%.
That means the spread of individual values has increased, Hence the SD will increase.
Sufficient.

Statement 2: The number of worms in each plot increased by the same percentage.
When the individual elements of a set are multiplied by a constant number, the new SD becomes constant times the old SD
The no of worms will always increase. Hence the SD.
Sufficient.

IMO Answer: D

This is yes no question.
Was the standard deviation of the number of worms per acre at the 15 sites higher at the end of the year?
In case of A answer is yes
In case of B answer is no
thus both choices answers the question stem Was the standard deviation of the number of worms per acre at the 15 sites higher at the end of the year?
thus answer is D

alitariquet: You are right.

My bad, the no of worms will always increase. Answer will be D
I'll edit my post right away.

Question stem:- Is SD>2000 ?

St1:- By the end of the year, the range of the number of worms per acre for the sites had increased by 20%.
Range=greatest no of worms-Least no of worms, is increased by 20%.
What about the individual data of #worms per acre in the respective sites?Are the no of worms at 15 sites close to mean no of worms? Are the no of worms at 15 sites spread-ed away from mean no of worms?

SD is a measure of standard dispersion of all the elements from the mean. The farther away the terms are from the mean, the larger the standard deviation.Similarly, the closer the terms are from the mean, the smaller the standard deviation.Since we don't have the information on either the mean or the nature of no of worms(increased each/decreased each) we can't say whether SD is decreased or increased when range is increased by any magnitude of percentage.
Insufficient.

St2:- The number of worms in each plot increased by the same percentage.
Note:- Decrease/increase in all elements of a set by a constant percentage will decrease/increase standard deviation of the set by the same percentage.
So, SD>2000
Sufficient.

Ans. (B)
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Question stem:- Is SD>2000 ?

St1:- By the end of the year, the range of the number of worms per acre for the sites had increased by 20%.
Range=greatest no of worms-Least no of worms, is increased by 20%.
What about the individual data of #worms per acre in the respective sites?Are the no of worms at 15 sites close to mean no of worms? Are the no of worms at 15 sites spread-ed away from mean no of worms?

well choice A says Range of no of worms per acre increase by 20% this means we have increase in worms in each acre not total range increase in 15 sites if A has to ruled out it must that " By the end of the year, the range of the number of worms per acre(removed) for the sites had increased by 20%
ie By the end of the year, the range of the number of worms for the sites had increased by 20%.

Hi alitariquet,
Here the #worms are measured in per acre only. UoM of #worms is worms/acre.

Per acre doesn't refer to each of the sites.
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Thanks for pointing out that was tricky

I was doing other related questions to S.D, just got to learn a correlation between S.D and range

i.e-S.D of certain list <=(1/2)range of that list.

Since A tells us that Range had increased, doesn't that mean S.D has Increased as well ?

Please correct me where i am going wrong

VeritasKarishma...

Could you please help analyse Statement I
Thanks in advance

There is no direct relationship between range and standard deviation. But because both are measures of spread, the range can help (depending on the data) to draw conclusions about the SD.

This is a great question to clarify concepts on standard deviation (SD). Statement 1 plays on the concept of range and tries to link it to standard deviation. Increase in range does not mean an increase in the SD. We need to consider the other terms other than the highest and lowest terms. What if the last/highest term has moved 20 percent further away from the first/lowest term but all the other terms have come much closer to the mean. In that case, an increase in range will not lead to an increase in SD. So we get a NO answer for the question.
We can get a YES answer relatively easily by considering an increase of 20 percent in all the terms above the mean. Since they are higher than the mean, an increase would push them further away from the mean, thereby increasing the standard deviation.
So Statement 1 is NOT SUFFICIENT.

Regards,
Udit

For the purposes of the GMAT:
Standard deviation = average distance from the mean

Statement 1:
Here, we know only that the distance between the smallest and largest values increased by 20%.
No way to determine whether FOR ALL 15 VALUES the average distance from the mean increased.
INSUFFICIENT

Statement 2:
Since each data point increased by \(x\)%, the average distance from the mean increased by \(x%\)%.
Thus, the answer to the question stem is YES.
SUFFICIENT


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IMO [B] because when you multiply the numbers of a set by a number, the SD of the set increases by that same number

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