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What is the SD?

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Jul 11, 2014 6:44 pm
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

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Brent
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by GMATinsight » Fri Jul 11, 2014 9:25 pm
Standard Deviation depends on the deviation of the terms in set from mean of the set
i.e. ZERO deviation of terms from mean means ZERO Standard Deviation
i.e. GREATER deviation of terms from mean means GREATER Standard Deviation

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.

If Mean = Highest Number then the deviation of other numbers from mean has to be zero and all the numbers of set must be same therefore Standard deviation must be Zero.
(We can try by taking some arbitrary numbers as well for example if the mean = 3 then highest =3
and sum of numbers = 3x5 = 15 then all numbers must be 3 only)
SUFFICIENT

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

Order received daily = 0 that mean all the terms of set are equal leading to Zero Standard deviation
SUFFICIENT

Answer: Option D
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