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Standard Deviation

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by lukaswelker » Thu Apr 17, 2014 8:24 am
hey guys

I just have a doubt regarding the sufficiency of the first.

Here goes the question,

Web site W receives orders for its products every day. What is the standard deviation of the numbers of orders that Web site W received for the past 5 days?

(1) the average (arithmetic mean) number of orders that Web site W received per day for the past 5 days is equal to the greatest numbers of orders that Web site W received daily for the past 5 days.

(2) The range of numbers of orders that Web site W received daily for the past 5 days is equal to 0.

Does anybody knows a good method to make sure I don't do the same mistake again?

Many thanks
Lukas
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Apr 17, 2014 9:31 am
lukaswelker wrote: Website W receives orders for its products every day. What is the standard deviation of the numbers of orders that Website W received for the past 5 days?

(1) The average (arithmetic mean) number of orders that Web site W received per day for the past 5 days is equal to the greatest numbers of orders that Web site W received daily for the past 5 days.

(2) The range of numbers of orders that Web site W received daily for the past 5 days is equal to 0.
IMPORTANT: When it comes to Standard Deviation, the GMAT LOVES to test one's knowledge of the fact that standard deviation = 0 when all of the numbers in a set are identical.

Target question: What is the standard deviation of the numbers of orders that Website W received for the past 5 days?

Statement 1: The average (arithmetic mean) number of orders that Website W received per day for the past 5 days is equal to the greatest numbers of orders that Website W received daily for the past 5 days.
This tells us that the website received the SAME NUMBER of orders each day. Here's why:
Let M = the mean
So, the SUM of all five days' orders = 5M

We already know that M is equal to the largest number of orders.
In order to get a SUM of 5M, none of the days' orders can be less than M.
So, the website received the SAME NUMBER of orders each day.
If all 5 values (orders each day) are the same, then the standard deviation MUST be 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The range of numbers of orders that Web site W received daily for the past 5 days is equal to 0.
If the range = 0, then the website received the SAME NUMBER of orders each day.
If all 5 values (orders each day) are the same, then the standard deviation MUST be 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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