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

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

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

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 !!

how did u calculate the standard deviation to be 3?

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!

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

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

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