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

Question

A local municipality did a census of earthworms per acre of soil for 15 similar sites and found that the standard deviation of the number of worms per acre was 2,000. Was the standard deviation of the number of worms per acre at the 15 sites higher at the end of the year?

(1) By the end of the year, the range of the number of worms per acre for the sites had increased by 20%.

(2) The number of worms in each plot increased by the same percentage.

PKN · Accepted Answer

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)

GmatDaddy · Answer

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

epiphany1 · Answer

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

GmatDaddy · Answer

alitariquet : You are right.

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

epiphany1 · Answer

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%.

PKN · Answer

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.

epiphany1 · Answer

Thanks for pointing out that was tricky

anmolsd1995 · Answer

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

Debashis Roy · Answer

VeritasKarishma ...

Could you please help analyse Statement I
Thanks in advance

Sejal16 · Answer

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.

uc26 · Answer

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

GMATGuruNY · Answer

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

B

robotman88 · Answer

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

akshatv45 · Answer

To understand if standard deviation has increased or decreased, we need to know the spread of the data and not just the range.

lets take a smaller example and say earlier no. of worms were {1,2,3,4,5,6,7,8,9,11} in 10 sites.
By year end range increased by 20% so {1,2,3,4,5,6,7,8,9,10,13} in 10 sites. In this case the standard deviation will increase.

But we don't know the spread. So the data points could be {1,2,3,4,5,6,7,8,9,11} at the census and {1,2,2,2,2,2,2,2,2,13} at the end of the year. In this case the standard deviation will decrease.

So to be sure about the increase in std. deviation we should know the spread. This is captured in the second statement and hence it is sufficient where as statement 1 is not.

BinodBhai · Answer

No, statement (1) is **not sufficient** to answer the question.

Here's why:

* **Standard Deviation vs. Range:**
 * **Range** is the difference between the maximum and minimum values in a dataset.
 * **Standard Deviation** measures the average spread or dispersion of data points around the mean.
* **Relationship between Range and Standard Deviation:** While an increase in the range *can* sometimes indicate an increase in standard deviation, it's not a direct or guaranteed relationship.
 * Consider a scenario where the minimum value decreases significantly and/or the maximum value increases significantly, leading to a larger range. However, the data points in between might have clustered more tightly around the mean, potentially leading to a *smaller* standard deviation.
 * Conversely, the range might stay the same, but the data points could have spread out more evenly, increasing the standard deviation.

Therefore, knowing only that the range increased by 20% does not give us enough information to determine if the standard deviation also increased.

Hence (B)

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

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

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