Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

62% (06:19) correct
38% (01:33) wrong based on 49 sessions

HideShow timer Statistics

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.

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. Answer: E.

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. Answer: A.

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 Answer: 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 Answer: C.

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.

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 Answer: A.

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. Answer: D.

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. Answer: B.

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. Answer: A.

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

Show Tags

15 Dec 2009, 10:55

Bunuel wrote:

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.

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

Show Tags

19 Dec 2009, 21:44

3

This post received KUDOS

1

This post was BOOKMARKED

I'll try to provide some explanation of the questions with reference to answers, please correct me if i'm wrong.

Thanks

ANSWERS (OA):

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. Answer: E.

Reason : As none of the information above is adequate to find the SD, therefore SD is not possible to calculate

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. Answer: A.

Reason: A is the right answer as we know from the Stmt 1 the total number of members in the set and consecutive integers shows that they're not identical so we can calculate the SD from this statement. Stmt 2 is not sufficient as with median we can't calculate SD.

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 Answer: D.

Reason: This is the same problem which is also asked in the PS problem. If the distribution is symmetric about the mean then it means that 50% of the population is above and below the mean.

Stmt 1: if 68% population is within one SD of the mean then 34% is either above or below the mean. Out of 100, 32% population is outside 1SD of the mean so 16% of the population is m+d as well as 16% as m-d.

Stmt2: also reflects the same thing that 16% population is below m-d so both of them are sufficient.

4. Set A and B are 2 sets of numbers. A has a standard deviation 3 and a mean 5. B has the same mean but standard deviation 4. Can we find the standard deviation of the set A U B ? If no, then is it possible with the following additional information? (1) Both sets have the same number of members each (let’s say 4) (2) Both sets have distinct members (no number is common to both sets). Answer: A.

Reason: A is the option as with the help of the Stmt 1 we know the total members of the set however Stmt 2 means distinct members so the set wont be AUB then it will be AnB.

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 Answer: C.

Reason: Stmt 1 S = {25,30,40,50,x} Mean = 40 then x = 55

Stmt 2 T = {x,30,40,45,50} Mean = 40 then x= 35

So with the help of both stmts Set S has greater SD than T, that is why C is the answer

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

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 Answer: A.

Stmt 1: if the range of the set is not equal to zero then SD will not be zero it will be greater than zero. Stmt 2: Mean can be 5 but set may contain identical elements.

So A is right but SD will not be zero.

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. Answer: D.

Both stmt are sufficient as with Stmt 1 we know that range is zero so the third term will be 3 and with the stmt 2 it shows that SD = 0 so third term will be 3.

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. Answer: B.

May be i don't understand the question properly, B is the right choice as each of the nest have identical eggs therefore SD = 0 or i missed something

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. Answer: A.

As 30% of the volume is removed from all the tanks so SD remains same. therefore stmt 1 is sufficient.
_________________

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

Show Tags

23 Dec 2009, 03:30

Bullet wrote:

I'll try to provide some explanation of the questions with reference to answers, please correct me if i'm wrong.

Thanks 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? [/b](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. Answer: B.

[b]

May be i don't understand the question properly, B is the right choice as each of the nest have identical eggs therefore SD = 0 or i missed something

hi Bullet, really nice explanation by u..

Q10) totally there are 10 nests with some number of eggs. SD=?? 1) avg. number of eggs for 10 nests is 4, i.e total of 40 eggs. But, this does not provide us with the number of eggs in each nest. So, SD can vary. Hence, data insuff. 2) each nest contained same number of eggs. when the elements in a set are identical SD=0. so, in this case SD=0. data suff.

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

Show Tags

08 Jun 2010, 07:17

4. Set A and B are 2 sets of numbers. A has a standard deviation 3 and a mean 5. B has the same mean but standard deviation 4. Can we find the standard deviation of the set A U B ? If no, then is it possible with the following additional information? (1) Both sets have the same number of members each (let’s say 4) (2) Both sets have distinct members (no number is common to both sets).

Can we have the explaination for this problem?
_________________

Want to improve your CR: http://gmatclub.com/forum/cr-methods-an-approach-to-find-the-best-answers-93146.html Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

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

Show Tags

03 Oct 2010, 02:13

Quote:

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. Answer: A.

As 30% of the volume is removed from all the tanks so SD remains same. therefore stmt 1 is sufficient.

Quote:

The Std Dev does NOT remain the same but ALso decreases by 30% as All subjects decrease by 30% hence ans is A

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

Show Tags

09 Oct 2010, 17:00

1

This post received KUDOS

Quote:

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? [/b](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. Answer: A.

As 30% of the volume is removed from all the tanks so SD remains same. therefore stmt 1 is sufficient.

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.

Answer is A. But, the SD will decrease by 30%.
_________________

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

Show Tags

18 Nov 2010, 08:38

1

This post was BOOKMARKED

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.
_________________

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.

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

Show Tags

24 Nov 2010, 05:57

BlitzHN wrote:

Quote:

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? [/b](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. Answer: A.

As 30% of the volume is removed from all the tanks so SD remains same. therefore stmt 1 is sufficient.

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.

Answer is A. But, the SD will decrease by 30%.

I agree. The new Sd will be 0.7*original Sd or in other terms it drops by 30%. Sqrt(1/n*sum(0.7x-0.7*mean)^2), you can take 0.7 out of the sqrt and hence the new sd is 0.7 times the old.

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

Show Tags

05 Jan 2011, 17:36

Hi Bunuel,

I'd like to discuss question 9 a bit further. If the standard deviation of a set is 4, then the range within that SD is always 8, no matter you go the the left or right. Both (1) and (2) are redundant to answer the question right?

I'd like to discuss question 9 a bit further. If the standard deviation of a set is 4, then the range within that SD is always 8, no matter you go the the left or right. Both (1) and (2) are redundant to answer the question right?

I see your point. The question is quite ambiguous and different interpretations are possible. Actually depending on how you interpret the question the answer can be B, D or even E. So, I'm deleting this question from the set.
_________________

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

Show Tags

04 Apr 2011, 07:52

1

This post received KUDOS

1

This post was BOOKMARKED

adhithya wrote:

not sure about answer of q2,a) says that there are 21 members in the set,but since we expect a unique value for std deviation we must choose option c

1. Any set of 21 consecutive numbers will have exact same standard deviation, irrespective of its value. Std dev for \({1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21} = 6.0553\) Std dev for \({11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31} = 6.0553\) Believe this is true for all evenly spaced sets with equal numbers of elements and same common difference. Sufficient.

2. Set can be: {19,20,21}. Median=20. Std Dev=0.8165 {15,16,17,18,19,20,21,22,23,24,25}. Median=20. Std Dev=3.16228 Not Sufficient.

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...