Which of the Following Data Sets has the Third Largest Standard Deviation? GMAT Problem Solving

Question: Which of the following data sets has the third largest standard deviation?

(A) {1, 2, 3, 4, 5}
(B) {2, 3, 3, 3, 4}
(C) {2, 2, 2, 4, 5}
(D) {0, 2, 3, 4, 6}
(E) {-1, 1, 3, 5, 7}

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

In this task, we need to identify the set with the third greatest SD, i.e., the set where the data points are the third most prevalent. SD measures the amount of variance from the mean in a particular set.

Just now, I determined any gaps or variations between each set's subsequent pieces.
A) 1,1,1,1 (3rd highest SD)
B) 1,0,0,1
C) 0,0,2,1
D) 2,1,1,2 (2nd highest SD)
E) 2,2,2,2 (1st highest SD)

Hence the answer choice A is correct.

Approach Solution 2:

We need to compare 'standard deviation'. So, we should look out for similarities between all the sets.

The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...

Now we have 5 different sets which have an average of 3, so we will look for the spread of the other elements of the set around the average.
clearly, E has a range of 7-(-1) or 8, and has the highest standard deviation.
Next is D, which has a range of 6-0 or 6..
and THIRD is A

Hence, the answer is Option A.

Approach Solution 3:

(A) {1, 2, 3, 4, 5}
= 2 1 1 2 = 6/4

(B) {2, 3, 3, 3, 4}
= 1 0 0 1 = 2/4

(C) {2, 2, 2, 4, 5}
= 0 0 2 3 = 5/4

(D) {0, 2, 3, 4, 6}
= 3 1 1 3 = 8/4

(E) {-1, 1, 3, 5, 7}
= 4+2+2+4 = 12/4

The 3rd highest Standard Deviation is A)

“Which of the Following Data Sets has the Third Largest Standard Deviation?” - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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