Given that the mean of Set A is 10, what is the range of two

Question

Given that the mean of Set A is 10, what is the range of two standard deviations above and below the mean?

(1) One standard deviation above and below the mean ranges from 7 to 13.

(2) The median of set A is 11.

watwazdaquestion · Accepted Answer

1. standard deviation = 3 since mean = 10... 3 units below and 3 units above. can calculate range of 2 standard deviations above and below mean by: 10-6 = 4 and 10+6 = 16... range of 2 standard deviations above and below mean = (4, 16)
2. gives no information on standard deviation. insufficient.

answer is A

Bunuel · Answer

Similar questions to practice: 70-75-80-85-90-105-105-130-130-130-the-list-shown-consist-of-100361.html the-standard-deviation-of-a-normal-distribution-of-data-is-99221.html for-a-certain-exam-a-score-of-58-was-2-standard-deviations-b-128661.html Hope it helps.

Sachin9 · Answer

how did u calculate the standard deviation to be 3?

Kris01 · Answer

1. says that 1 standard deviation above and below the mean ranges from 7 to 13. Calculate the range. Range=6.

Now, standard deviation for a set is constant. Let us draw a number line.

---------|----------------|---------------|------------------ 
 -m mean +m

In this line segment, mean is at the center and the distance between 2 equal points -m and +m from mean is 6. These two points are equidistant as they are mentioned to be one standard deviation above and below the mean. Hence, the range of values between them=2m
2m=6
Hence, m=3

Hope this clarifies any doubts!

neeti1813 · Answer

The solutions provided above are still not clear. Could someone please make an attempt to give a detailed solution as I am very weak at mean median mode problems :roll:

WoundedTiger · Answer

Hi Neeti, You need to review basics. Go through the link below and then comeback to the question to see if you can answer it math-standard-deviation-87905.html

rhine29388 · Answer

Statement 1 states that 7 is one standard deviation below the mean and 13 is one standard deviation above the mean , clearly we can calculate range of two standard deviations above and below the mean which would be 
lower range below mean - 4 
upper range above mean - 16 
So clearly sufficient
Statement 2 states the median of the set which is of no use in standard deviation calculations so clearly inufficient
correct answer - A

ScottTargetTestPrep · Answer

We are given that the mean of set A is 10, and we need to determine the range of two standard deviations above and below the mean. If we let s = the standard deviation, we need to calculate:

10 + 2s - (10 - 2s)

If we simplify this expression, we have 4s. That is, if we can determine the standard deviation, we can determine the value of 4s.

Statement One Alone:

One standard deviation above and below the mean ranges from 7 to 13.

Using the information in statement one, we can say that 10 - s = 7 and 10 + s = 13. Solving s in either equation, we have s = 3. Thus, 4s = 12.

Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The median of set A is 11.

Knowing the median of the set is not enough information to determine the standard deviation. Statement two alone is not sufficient to answer the question.

Answer: A

debtanuB · Answer

Actually its a simple question if you understand what exactly it is trying to tell you?? Mean(m)=10 (Given) ; Asked=Range of two std. dev. above & below mean ,i.e, (m-2d) & (m+2d) ?? From, (1) its clear (m-d) & (m+d) are 7 & 10 respectively ; Therefore, (m-d)=7 =>d=10-7=3 =>m-2d & m+2d are (10-2x3) & (10+2x3) OR 4 & 16 respectively; Hence, (1) is SUFFICIENT ; From, (2) we get no clue about std. dev. as it talks about median only ; Hence, (2) is INSUFFICIENT ; Thus, answer is option A ; All the best !!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Given that the mean of Set A is 10, what is the range of two

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Given that the mean of Set A is 10, what is the range of two

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards