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Standard Deviation (SD) Data Sufficiency - March 28, 2005
Directions
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 -
| 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 to answer the question asked. |
| 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 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
What is the standard deviation (SD) of the four numbers p, q, r, 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
The correct choice is (C). The correct answer is that both the statements together are sufficient)
Explanatory Answer
The question asks one to find the standard deviation of four numbers.
Standard deviation =
Statement (1) gives the information about the sum of the 4 numbers. Hence, the mean of the four numbers is 6 and the square of the mean of the numbers is 36. However, this statement does not provide any information about the mean of the squares of the numbers. Hence, statement (1) alone is not sufficient.
Statement (2) gives the sum of the squares of the 4 numbers. Hence, the mean of the squares of the numbers is 61. However, this statement does not provide any information about the square of the mean of the numbers. Hence, statement (2) alone is not sufficient.
When the information provided in the two statements are combined, one can find the standard deviation of the four numbers. Hence, answer is choice (C ).
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