Distribution D consists of five different numbers. What is the standar

Question

Data set D consists of five different numbers. What is the standard deviation of data set D ?

(1) The average of the five numbers in data set D is 12.

(2) The range of the five numbers in data set D is 12

CrackverbalGMAT · Answer

Statement 1:  The average of the five numbers in data set D is 12.

The sum of observations = 60

5 + 7 + 15 + 16 + 17 = 60

5 + 9 + 14 + 15 + 17 = 60

The standard deviations for both the sets will be different (4.98 and 4.38 respectively)

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E

Statement 2:  The range of the five numbers in data set D is 12

5, 7, 15, 16, 17 The range is 12

5, 9, 14, 15, 17 The range is 12

Since the data values are different, the standard deviations will be different.

Therefore Statement 2 Alone is Insufficient  . Answer Options could be C or E

Combining Both Statements:

5, 7, 15, 16, 17 The range is 12 and the sum is 60

5, 9, 14, 15, 17 The range is 12 and the sum is 60.

Again we get 2 different standard deviations as the data values are different

Therefore Both Statements together are Insufficient  .

Option E

Arun Kumar

IanStewart · Answer

You'd need to know about the numbers in the middle of the set to calculate its standard deviation. Here, using both Statements, the data set could be:

6, 7, 12, 17, 18

which has a bigger standard deviation (because the values are generally further from the mean) than this other possibility:

6, 11, 12, 13, 18

so the answer is E.

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 4 or more variables: Let the original condition in a DS question contain 4 or more variables. Now, 4 or more variables would generally require 4 or more equations for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 4 or more equations to match the numbers of variables and equations in the original condition, the logical answer is E.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

=> Let the Data set D has '5' numbers be 'a', 'b', 'c', 'd' , and 'e': D = {a, b, c, d, e}
=> We have to find 'Standard Deviation of D' ?.

Second and the third step of Variable Approach: From the original condition, we have 5 variables (a, b, c, d, and e).To match the number of variables with the number of equations, we need 5 more equations. Since conditions (1) and (2) will provide 2 equations, E would most likely be the answer.

Let’s take look at both condition together.

Condition(1) tells us that the average of the five numbers in data set D is 12.

Condition(2) tells us that the range of the five numbers in data set D is 12.

=> Average of '5' numbers is '12' and hence sum = 5 * 12 = 60 and Range is 12 so H - L = 12

=> Possible combinations: [4 , 12, 13, 15, 16], [6 , 11, 12, 13, 18]

=> For both the combinations, S.D. will be different.

Since the answer is not unique , both conditions combined together are not sufficient by CMT 2.

Both conditions combined together are not sufficient.

So, E is the correct answer.

Answer: E

SAVE TIME: By Variable Approach, when you know that we need two equations, we will directly combine the conditions to solve. We will save time in not checking the conditions individually.

Distribution D consists of five different numbers. What is the standar

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GMAT Data Sufficiency (DS) Questions

Distribution D consists of five different numbers. What is the standar

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