1> if the mean of a data set is 75 and the standard deviation (SD) is 10, what is the range of scores that fall within one SD of the mean?



2> If y=ax+b, and if teh SD of x series is S, what is the SD of Y series?


3> If ax+by+c=0, and if the SD of X series is S, what is the SD of Y series?


4>If sets X and Y have an equal number of elements, does set X have a greater SD that set Y?
a> The difference between each pair of the neighboring elements is consistent throughout each set.

b> Each of the first two elements in set Y is twics greater than the corresponding first and second elements is set X

SD of y will be aS.
Taking case if x is 0,1,2,3,4..... SD is S
now for series 1,2,3,4,5....... SD is S still (SD remains same if we add same number in all digits)
but for series 0,5,10,15,20,..... SD is 5S (SD becomes constant*OLD SD when all digits are multiplied by same constant).

a: Not enough SD of both sets cannot be determined.
b: Not enough SD of both sets cannot be determined.
Combining,
we can infer difference of X is (b-a) then of Y is 2(b-a) and it is consistent throughtout so SD can be calculated hence Sufficient so C.

4>If sets X and Y have an equal number of elements, does set X have a greater SD that set Y?
a> The difference between each pair of the neighboring elements is consistent throughout each set.

b> Each of the first two elements in set Y is twics greater than the corresponding first and second elements is set X

ANSWER SHOULD BE E

1 1 1
2 2 2 meets both condition and SD(X)=SD(Y)

For # 4, the answer should be A. Standard deviation depends on the differences between the elements regardless of the mean. These two sets meet the conditions of statement one and must have the same standard deviation:
Set one: 2,4,6,8,10
Set two: 19, 21, 23, 25, 27
Statement 2 does not tell us about elements in each set beyond the 2nd element.

4 combining a and b

sets can be (1,2,3) and (2,4,6) or (1,1,1) and (2,2,2). thus giving different SD's.

hence E it is.
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These questions are all terribly worded. My best advice is just to skip them. The first question misuses the word 'range' (the range is the difference between the largest and smallest numbers in a set; they mean to ask for the interval of scores which are within one standard deviation of the mean); the second and third questions misuse the word 'series' (a series in mathematics is a sum, and we take the standard deviation of sets, not of sums), and regardless those questions make no mathematical sense. The GMAT will never test standard deviation in the way these questions are attempting to test it. I discussed what those questions are attempting to ask in a different post, and explained what takeaways are actually useful on the GMAT (scroll way down):

pls-explain-them-frnds-110985.html

The fourth question is ambiguous. First, sets are not in any order, so it makes no sense to talk about the 'first element' in a set. We also don't say 'twice greater' (technically that means 'three times as much', but you would never see that phrase on the GMAT); we just say 'twice'. Finally, in Statement 1, when they say 'consistent', it's not clear what that means. I think they mean to say that each set is equally spaced, in which case they should use the word 'equal', not 'consistent'.

I'm not sure where these questions are from, but if the original source contains questions like these, it will be more confusing than helpful to use it for your preparation.
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Yes, 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.

For example: if the standard deviation of set A={1, 11, 15} is d then the standard deviation of the following sets B={6, 16, 20} and C={0, 10, 14} is also d (set B obtained by adding 5 to each of the element of set A and set C is obtained by subtracting -1 to each of the element of set A).

On the other hand if we increase or decrease each term in a set by the same percent (multiply by some constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

For example: if the standard deviation of set A={1, 11, 15} is d then the standard deviation of the following sets B={2, 32, 30} is 2d (set B obtained by multiplying each of the element of set A by 2 (increasing by 100%)).

More tips on SD:
ps-questions-about-standard-deviation-85897.html (collection of PS questions on SD)
lately-many-questions-were-asked-about-the-standard-85896.html (collection of DS questions on SD)
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Merging similar topics.

Note that those are not quality questions as Ian notes above, so I wouldn't worry about them at all. See above post for some tips on SD (which are related to these questions).

Generally for the GMAT you only need to understand the concept of SD: you won't be asked to actually calculate the standard deviation of a set on the GMAT. So, what is the main thing you should know about it? Standard deviation shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

Check this for more: math-standard-deviation-87905.html

PS questions on SD: ps-questions-about-standard-deviation-85897.html
DS questions on SD: ds-questions-about-standard-deviation-85896.html

Hope it helps.

Hope it helps.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates