A GMAT data sufficiency (DS) question in Descriptive Statistics. Concept tested includes grasp of basics of standard deviation and average.

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
- BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
- EACH statement ALONE is sufficient to answer the question asked.
- Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

##### Numbers

All numbers used are real numbers.

##### Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

##### Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

#### Question: If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?

- m > a
- a + b + c + d = 0

#### Video Explanation

Scroll down for explanation text#### Explanatory Answer

#### What kind of an answer will the question fetch?

The question is an "Is" question. Answer to an "is" questions is either YES or NO.

#### When is the data sufficient?

The data is sufficient if we are able to get a DEFINITE Yes or No.

If the statements do not have adequate data to determine whether the standard deviation is greater than 0, the data is NOT sufficient.

#### When will the standard deviation be 0?

The standard deviation, s, will be 0 in two instances.

- when all the elements in the set are the same
- the set contains only one element, which in this case is not possible.

#### Statement 1: m > a

If a = b = c = d, the average m will be the same as a.

Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.

Statement 1 ALONE is sufficient.

Eliminate choices B, C and E. Choices narrow down to A and D.

#### Statement 2: a + b + c + d = 0

**Approach**: Look for a counter example

Example: When a = b = c = d = 0, s = 0

Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0

Statement 2 ALONE is NOT sufficient.

Eliminate choice D. Choice A is the answer.

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