GMAT Question  >  What is the standard deviation (SD) of the fo... Save

Related Test

What is the standard deviation (SD) of the four numbers p, q, r, and s?
(1) The sum of p, q, r, and s is 24.
(2) The sum of the squares of p, q, r, and s is 224.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
  • d)
    EACH statement ALONE is sufficient to answer the question asked;
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed. 
Correct answer is option 'C'. Can you explain this answer?

Answers

Standard deviation = √Mean of squares of the numbers−square of mean of the numbers
Evaluating Statement (1) ALONE: The sum of p, q, r, and s is 24.
From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.
We need additional information to find the SD.
This statement does not provide any information about the mean of the squares of the numbers.
Statement 1 alone is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C, or E.
Evaluating Statement (2) ALONE: The sum of the squares of p, q, r, and s is 224.
Hence, the mean of the squares of the numbers is 56.
However, this statement does not provide any information about the square of the mean of the numbers.
Statement 2 alone is NOT sufficient.
Eliminate choice B. Choices narrow down to C and E.
Evaluating the statements together.
From statement 1 we know that the square of the means is 36.
From statement 2 we know that the mean of the squares is 56.
Using the formula,
Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,
we can find the SD of the 4 numbers.
Statements together are sufficient. Choice C is the answer.

View courses related to this question
Explore GMAT courses
Explore GMAT courses
View courses related to this question
1 Crore+ students have signed up on EduRev. Have you?

Similar GMAT Doubts

  • NumbersAll numbers used are real numbers.FiguresA figure accompanying a dat... more

  • 1 Answer

  • NumbersAll numbers used are real numbers.FiguresA figure accompanying a dat... more

  • 1 Answer

Question Description
What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?.
Solutions for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer?, a detailed solution for What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice What is the standard deviation (SD) of the four numbers p, q, r, and s?(1) The sum of p, q, r, and s is 24.(2) The sum of the squares of p, q, r, and s is 224.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;d)EACH statement ALONE is sufficient to answer the question asked;e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
Standard deviation = √Mean of squares of the numbers−square of mean of the numbersEvaluating Statement (1) ALONE: The sum of p, q, r, and s is 24.From the information in statement 1 we can find the mean of the four numbers to be 6 and the square of the mean of the numbers to be 36.We need additional information to find the SD.This statement does not provide any information about the mean of the squares of the numbers.Statement 1 alone is NOT sufficient.Eliminate choices A and D. Choices narrow down to B, C, or E.Evaluating Statement (2) ALONE: The sum of the squares of p, q, r, and s is 224.Hence, the mean of the squares of the numbers is 56.However, this statement does not provide any information about the square of the mean of the numbers.Statement 2 alone is NOT sufficient.Eliminate choice B. Choices narrow down to C and E.Evaluating the statements together.From statement 1 we know that the square of the means is 36.From statement 2 we know that the mean of the squares is 56.Using the formula,Standard deviation = √Mean of squares of the numbers−square of mean of the numbers,we can find the SD of the 4 numbers.Statements together are sufficient. Choice C is the answer.