TANCET 2014 DS 73: Statistics

Directions for Data Sufficiency Questions

The question is followed by 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 problem plus your knowledge of mathematics and everyday facts, choose the answer as:

Choice 1 if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Choice 2 if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Choice 3 if both the statements (1) and (2) TOGETHER are sufficient, but NEITHER statement alone is sufficient.
Choice 4 if each statement ALONE is sufficient.
Choice 5 if statements (1) and (2) TOGETHER are not sufficient, and additional data is needed.

Question

Medium Data Sufficiency

If the first term of the data set {x, y, z} is 3, what is the third term?

Statement 1: The range of this data set is 0.
Statement 2: The standard deviation of this data set is 0.

Correct Answer Choice (4). Each statement is INDEPENDENTLY sufficient.

Explanatory Answer - step by step

Question Statement (1) Alone Statement (2) Alone Tabs

What should we know from the Question Stem?

Before evaluating the two statements, answer the following questions to get clarity on when the data is sufficient.

What kind of an answer will the question fetch?

The question is "What is the third term?"

The answer to should be a number. For e.g., 5.

When is the data sufficient?

If we are able to come up with a UNIQUE answer, the data is sufficient.

If we are not able to come up with a UNIQUE number, the data is NOT sufficient.

What theoretical concepts should we know at this stage?

The range for a data set is the difference between the highest and the least term.

Example: Let the data set be {45, 2, 7, 9, 1}. The highest term is 45. The least term is 1. The range is 44.
Statement (1) ALONE

The range of this data set is 0.

From the question stem, we know that the first term is 3.

If the range of the data set is 0, then the difference between the highest and the least term is 0. i.e., the highest and the least term are the same.

In other words, all terms of the data set are the same.

Therefore, the 3rd term will also be 3.

We could get a UNIQUE answer to the question with statement 1.

Statement (1) ALONE is sufficient.

If statement (1) ALONE is sufficient, we can narrow our choices to 1 or 4.
Statement (2) ALONE

The standard deviation of this data set is 0.

What does it mean?

If the standard deviation is 0, then the terms of the data set do not deviate from the mean. i.e., all the terms of the data set are the same.

Because the 1st term is 3, all the terms should also be 3.

Using statement (2) ALONE we could get a UNIQUE answer to the question.

Statement (2) ALONE is ALSO sufficient.

If statement (1) ALONE is sufficient and statement (2) ALONE is ALSO sufficient, each statement is INDEPENDENTLY sufficient.

Hence, choice (4) is the answer.