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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  [#permalink]

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New post 31 Aug 2018, 23:04
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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.

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A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post Updated on: 01 Sep 2018, 02:05
Bunuel wrote:
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.


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
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Originally posted by GmatDaddy on 01 Sep 2018, 00:41.
Last edited by GmatDaddy on 01 Sep 2018, 02:05, edited 1 time in total.
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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 01:46
1
GmatDaddy wrote:
Bunuel wrote:
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.


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
Here, in our case, if the increase in the no of worms is greater than 100%, the SD will increase otherwise decrease.
Insufficient.

IMO Answer: A


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
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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 02:03
alitariquet: You are right.

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

alitariquet wrote:
GmatDaddy wrote:
Bunuel wrote:
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.


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
Here, in our case, if the increase in the no of worms is greater than 100%, the SD will increase otherwise decrease.
Insufficient.

IMO Answer: A


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

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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 19:37
1
1
Bunuel wrote:
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.


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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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 20:16
PKN wrote:
Bunuel wrote:
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.


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%.
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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 20:22
alitariquet wrote:
PKN wrote:
Bunuel wrote:
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.


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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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 01 Sep 2018, 20:32
Thanks for pointing out that was tricky
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A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 03 Feb 2019, 00:26
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
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Re: A local municipality did a census of earthworms per acre of soil for 1  [#permalink]

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New post 05 Feb 2019, 22:54
VeritasKarishma...

Could you please help analyse Statement I
Thanks in advance
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Re: A local municipality did a census of earthworms per acre of soil for 1   [#permalink] 05 Feb 2019, 22:54
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