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DS questions about standard deviation

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Re: DS questions about standard deviation  [#permalink]

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New post 19 Dec 2016, 04:46
Keats wrote:
Hi Bunuel

Can you please post your explanation to Q7. Someone has explained it on page 1, but I'd like to see as to how you approach the question.

I am posting it here for your convenience again.

Set X consists of 8 integers. Is the standard deviation of set X equal to zero?

(1) The range of set X is equal to 3
(2) The mean of set X is equal to 5


Check here: set-x-consists-of-8-integers-is-the-standard-deviation-of-67893.html
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New post 10 Jun 2017, 10:01
2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

Hi Banuel,
I have a question on the the above SD, Everyone is saying answer is A,
But,
The question itself is giving the answer without need of choices, coz, he gave a set of consecutive integers, which means SD is 1. You cannot assume all are different or all are same. I don't need 1 or 2 to decide it right?

Can you please explain me.
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New post 10 Jun 2017, 10:13
sasidharrs wrote:
2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

Hi Banuel,
I have a question on the the above SD, Everyone is saying answer is A,
But,
The question itself is giving the answer without need of choices, coz, he gave a set of consecutive integers, which means SD is 1. You cannot assume all are different or all are same. I don't need 1 or 2 to decide it right?

Can you please explain me.


No, that's not correct. Sets with different number of elements will give different standard deviation. The SD of {1, 2} is different from that of {1, 2, 3, 4, 5, 6}
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DS questions about standard deviation  [#permalink]

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New post 29 Oct 2017, 16:25
3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d

Hi Bunuel,

Can you please explain the solution of this question?
How are both statements Sufficient?
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New post 29 Oct 2017, 20:31
radhikakhemka007 wrote:
3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d

Hi Bunuel,

Can you please explain the solution of this question?
How are both statements Sufficient?


The lifetime of all the batteries produced by a certain company in a year have a distribution that is symmetric about the mean m. If the distribution has a standard deviation of d, what percent of the distribution is greater than m+d?

Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

(1) 68% of the distribution lies in the interval from m-d to m+d, inclusive --> 100%-68%=32% is less than m-d and more than m+d. As distribution is symmetric about the mean then exactly half of 32%, or 16%, would be more than m+d. Sufficient.

(2) 16% of the distribution is less than m-d --> again, as distribution is symmetric about the mean then exactly 16%, will be more than m+d. Sufficient.

Answer: D.

Hope it helps.
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Re: DS questions about standard deviation  [#permalink]

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New post 20 Nov 2018, 05:02
1
Bunuel wrote:
Lately, many questions were asked about the standard deviation. So I'm posting here my collection of DS problems on SD, plus some tips about it.

Please note the following:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.

Many questions below are easy, some are tough, but anyway they are good to master in solving SD problems. I'll post OA after some discussions. Please provide your way of thinking along with the answer. Thanks.

Here we go:

1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.

2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d

4. Question deleted

5. List S and list T each contain 5 positive integers, and for each list the average of the integers in the list is 40. If the integers 30,40 and 50 are in both lists , is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?
(1)The integer 25 is in list S
(2)The integer 45 is in list T

6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member

7. Set X consists of 8 integers. Is the standard deviation of set X equal to zero?
(1) The range of set X is equal to 3
(2) The mean of set X is equal to 5

8. {x,y,z}
If the first term in the data set above is 3, what is the third term?

(1) The range of this data set is 0.
(2) The standard deviation of this data set is 0.

9. Question deleted

10. A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

11. During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.


CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, m, of the values.
2. For each value xi calculate its deviation (xi-m) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.

TIPS:
1. |Median-Mean| <= SD.

2. Variance is the square of the standard deviation.

3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.

9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.


You can also check collection of PS questions of SD at: http://gmatclub.com/forum/ps-questions- ... 85897.html


Dear Moderator,
Can we move these good DS problems to the DS forum,from the PS forum? Thank you.
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Re: DS questions about standard deviation  [#permalink]

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New post 20 Nov 2018, 05:05
stne wrote:
Bunuel wrote:
Lately, many questions were asked about the standard deviation. So I'm posting here my collection of DS problems on SD, plus some tips about it.

Please note the following:
A. I was assured MANY TIMS, by various GMAT tutors, that GMAT won't ask you to actually calculate SD, but rather to understand the concept of it. Though KNOWING how it's calculated helps in understanding the concept.
B. During the real GMAT it's highly unlikely to get more than one ot two question on SD (as on combinatorics), actually you may see none, so do not spend too much of your preparation time on it, it's better to concentrate on issues you'll definitely face on G-day.

Many questions below are easy, some are tough, but anyway they are good to master in solving SD problems. I'll post OA after some discussions. Please provide your way of thinking along with the answer. Thanks.

Here we go:

1. What is the standard deviation of Company R’s earnings per month for this year?
(1) The standard deviation of Company R’s earnings per month in the first half of this year was $2.3 million.
(2) The standard deviation of Company R’s earnings per month in the second half of this year was $3.9 million.

2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

3. Lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. If the distribution has a standard deviation of d , what percentage of distribution is greater than m+d?
(1) 68 % of the distribution in the interval from m-d to m+d, inclusive
(2) 16% of the distribution is less than m-d

4. Question deleted

5. List S and list T each contain 5 positive integers, and for each list the average of the integers in the list is 40. If the integers 30,40 and 50 are in both lists , is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?
(1)The integer 25 is in list S
(2)The integer 45 is in list T

6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member

7. Set X consists of 8 integers. Is the standard deviation of set X equal to zero?
(1) The range of set X is equal to 3
(2) The mean of set X is equal to 5

8. {x,y,z}
If the first term in the data set above is 3, what is the third term?

(1) The range of this data set is 0.
(2) The standard deviation of this data set is 0.

9. Question deleted

10. A scientist recorded the number of eggs in each of 10 birds' nests. What was the standard deviation of the numbers of eggs in the 10 nests?
(1) The average (arithmetic mean) number of eggs for the 10 nests was 4.
(2) Each of the 10 nests contained the same number of eggs.

11. During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.


CALCULATING STANDARD DEVIATION OF A SET {x1, x2, ... xn}:
1. Find the mean, m, of the values.
2. For each value xi calculate its deviation (xi-m) from the mean.
3. Calculate the squares of these deviations.
4. Find the mean of the squared deviations. This quantity is the variance.
5. Take the square root of the variance. The quantity is th SD.

TIPS:
1. |Median-Mean| <= SD.

2. Variance is the square of the standard deviation.

3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.

9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.


You can also check collection of PS questions of SD at: http://gmatclub.com/forum/ps-questions- ... 85897.html


Dear Moderator,
Can we move these good DS problems to the DS forum,from the PS forum? Thank you.

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Re: DS questions about standard deviation  [#permalink]

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New post 15 Aug 2019, 01:32
During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

Can someone help me with the explanation.I see the answer is "A".If the initial volume of each of the tank is same then i can say A is correct.But he didn’t mention it anywhere.
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New post 15 Aug 2019, 01:34
tkalyan567 wrote:
During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?
(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

Can someone help me with the explanation.I see the answer is "A".If the initial volume of each of the tank is same then i can say A is correct.But he didn’t mention it anywhere.


Discussed in detail here: https://gmatclub.com/forum/during-an-ex ... 94166.html
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Re: DS questions about standard deviation  [#permalink]

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New post 23 Nov 2019, 21:58
Bunuel wrote:
shrive555 wrote:
Quote:
6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member
Answer: B.

Stmt 1 is not sufficient as all members are +ive but they may be identical so SD will be zero.
Stmt 2 has only one member so SD is zero

so that is why B is the answer


can't we reject statement 2 for the same reason as 1. Set consist of One number means SD is zero, Zero is neither positive nor negative.


I'm not sure understood your question but here is a solution for this problem:

Question asks "is standard deviation of T positive?" Now, \(SD\geq{0}\): the only case when standard deviation of a set equals to zero is when the set contains all identical elements (or which is same only 1 element). So, basically the question ask whether all elements of T are identical.


(1) All members of T are positive --> not sufficient, as we can have set {5, 5, 5} and SD will be zero or {5, 15, 25} and SD will be some positive number.
(2) T consists of only one member --> directly gives us the answer, as T consists of only one element then its SD will be 0. Sufficient.

Answer: B.

If the question is asking whether the SD>=0, then the first statement gives us values which can be zero or positive. So statement 1 should satisfy right??

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Re: DS questions about standard deviation  [#permalink]

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New post 23 Nov 2019, 22:03
[quote="Bunuel"][quote="sasidharrs"]2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

Hi Banuel,
I have a question on the the above SD, Everyone is saying answer is A,
But,
The question itself is giving the answer without need of choices, coz, he gave a set of consecutive integers, which means SD is 1. You cannot assume all are different or all are same. I don't need 1 or 2 to decide it right?

Can you please explain me.[/quote]

No, that's not correct. Sets with different number of elements will give different standard deviation. The SD of {1, 2} is different from that of {1, 2, 3, 4, 5, 6}[/quote]
Can we get an exact answer using statement 1??

[size=80][b][i]Posted from my mobile device[/i][/b][/size]
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DS questions about standard deviation  [#permalink]

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New post 24 Nov 2019, 02:06
ssshyam1995 wrote:
Bunuel wrote:
6. Set T consists of odd integers divisible by 5. Is standard deviation of T positive?
(1) All members of T are positive
(2) T consists of only one member


can't we reject statement 2 for the same reason as 1. Set consist of One number means SD is zero, Zero is neither positive nor negative.


I'm not sure understood your question but here is a solution for this problem:

Question asks "is standard deviation of T positive?" Now, \(SD\geq{0}\): the only case when standard deviation of a set equals to zero is when the set contains all identical elements (or which is same only 1 element). So, basically the question ask whether all elements of T are identical.


(1) All members of T are positive --> not sufficient, as we can have set {5, 5, 5} and SD will be zero or {5, 15, 25} and SD will be some positive number.
(2) T consists of only one member --> directly gives us the answer, as T consists of only one element then its SD will be 0. Sufficient.

Answer: B.
If the question is asking whether the SD>=0, then the first statement gives us values which can be zero or positive. So statement 1 should satisfy right??

Posted from my mobile device


Question asks "is standard deviation of T positive?"

(1) All members of T are positive --> not sufficient, as we can have set {5, 5, 5} and SD will be zero or {5, 15, 25} and SD will be some positive number.

So, as you can see the question does not ask, whether \(SD\geq{0}\), in this case we would not need the statements at all. SD is always more than or equal to 0. The question asks: is SD > 0.
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Re: DS questions about standard deviation  [#permalink]

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New post 24 Nov 2019, 02:45
ssshyam1995 wrote:
Bunuel wrote:
sasidharrs wrote:
2. What is the standard deviation of Q, a set of consecutive integers?
(1) Q has 21 members.
(2) The median value of set Q is 20.

Can we get an exact answer using statement 1??

Posted from my mobile device


Yes, but we don't need that for data sufficiency questions. All we need to get sufficiency, is to know that we CAN get a single numerical value for a DS question which asks for a specific question (value DS question).

If still interested, the SD for any set of 21 consecutive integers is \(\sqrt{\frac{110}{3}}\).

That question is discussed here: https://gmatclub.com/forum/if-q-is-a-se ... 51794.html
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Re: DS questions about standard deviation   [#permalink] 24 Nov 2019, 02:45

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