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## Web sites W

This topic has 4 expert replies and 1 member reply
rsarashi Master | Next Rank: 500 Posts
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#### Web sites W

Sat Sep 02, 2017 4:11 am
Web sites W receives order for its products every day. What is the standard deviation of the numbers of orders that Web sites W received daily 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 of the numbers of orders that Web site W received daily for the past 5 days.

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

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Scott@TargetTestPrep GMAT Instructor
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Mon Sep 11, 2017 10:34 am
rsarashi wrote:
Web sites W receives order for its products every day. What is the standard deviation of the numbers of orders that Web sites W received daily 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 of the numbers of orders that Web site W received daily for the past 5 days.

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

We need to determine the standard deviation of the numbers of orders that website W received daily for the past 5 days.

Statement One Alone:

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

The only way for the average of the number of orders to be equal to the greatest number of orders is if all the values are the same. Thus, the standard deviation is 0. Statement one alone is sufficient to answer the question.

Statement Two Alone:

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

Since the range is equal to zero, all the numbers of the orders are the same, and thus the standard deviation is 0. Statement two alone is sufficient to answer the question.

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GMATGuruNY GMAT Instructor
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Sun Sep 03, 2017 3:24 am
rsarashi wrote:
Hi GMATGuruNY ,

Thank you so much sir for the explanation.

Can we also this without letting the values?

If yes, then how please explain.

Thanks
Given a list of numbers:
If any value is LESS THAN THE AVERAGE, then at least one value must be GREATER THAN THE AVERAGE.
Statement 1 indicates that the greatest value is EQUAL to the average, implying that no value is GREATER than the average.
Since there is no value greater than the average, none of the values can be less than the average.
In other words:
All of the values must be equal to the average.
Since all of the values are equal, the standard deviation is 0.

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Sat Sep 02, 2017 5:36 am
rsarashi wrote:
Web sites W receives order for its products every day. What is the standard deviation of the numbers of orders that Web sites W received daily 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 of the numbers of orders that Web site W received daily for the past 5 days.

2) The range of the numbers of orders that Web site W received daily for the past 5 days is equal to 0.
In ascending order, let the 5 values = a, b, c, d, e.

Statement 1:
Let the average = 10, implying that the sum = (count)(average) = 5*10 = 50.
Thus:
a+b+c+d+e = 50.
Since the greatest value is equal to the average of 10, e=10.
The 5 orders are as follows:
a, b, c, d, e=10.
Since 10 is the greatest value, none of the other 4 values can be greater than 10.
Thus, the maximum possible case for the 5 values is as follows:
a=10, b=10, c=10, d=10, e=10.
In the list above, a+b+c+d+e = 50.
If any of the values in blue are decreased, the sum will be LESS THAN 50.
Thus:
To yield the required sum of 50, a=10, b=10, c=10, d=10, e=10.
The resulting list illustrates the following:
For the greatest of the 5 values to be equal to the average of the 5 values, all 5 values must be THE SAME.
Since all 5 values are the same -- implying that none of the 5 values deviates from the mean -- the standard deviation is 0.
SUFFICIENT.

Statement 2:
For the range to be 0, all 5 values must be the same.
Since all 5 values are the same -- implying that none of the 5 values deviates from the mean -- the standard deviation is 0.
SUFFICIENT.

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rsarashi Master | Next Rank: 500 Posts
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Sat Sep 02, 2017 11:25 am
Quote:
In ascending order, let the 5 values = a, b, c, d, e.

Statement 1:
Let the average = 10, implying that the sum = (count)(average) = 5*10 = 50.
Thus:
a+b+c+d+e = 50.
Since the greatest value is equal to the average of 10, e=10.
The 5 orders are as follows:
a, b, c, d, e=10.
Since 10 is the greatest value, none of the other 4 values can be greater than 10.
Thus, the maximum possible case for the 5 values is as follows:
a=10, b=10, c=10, d=10, e=10.
In the list above, a+b+c+d+e = 50.
If any of the values in blue are decreased, the sum will be LESS THAN 50.
Thus:
To yield the required sum of 50, a=10, b=10, c=10, d=10, e=10.
The resulting list illustrates the following:
For the greatest of the 5 values to be equal to the average of the 5 values, all 5 values must be THE SAME.
Since all 5 values are the same -- implying that none of the 5 values deviates from the mean -- the standard deviation is 0.
SUFFICIENT.

Statement 2:
For the range to be 0, all 5 values must be the same.
Since all 5 values are the same -- implying that none of the 5 values deviates from the mean -- the standard deviation is 0.
SUFFICIENT.

[/quote]Hi GMATGuruNY ,

Thank you so much sir for the explanation.

Can we also this without letting the values?

If yes, then how please explain.

Thanks

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sat Sep 02, 2017 1:56 pm
Hi rsarshi,

Standard Deviation is a relatively rare concept on Test Day (you'll likely see it in just one Quant question) and the GMAT will NEVER expect you to actually calculate it. As such, you really just need to understand the 'concept' of S.D. When a group of numbers is the same number over and over, then the S.D. = 0. As the group of numbers gets more 'spread out', the S.D. increases. That's all you really need to know to answer this question.

We're asked for the Standard Deviation of a group of 5 numbers.

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 of the numbers of orders that Web site W received daily for the past 5 days.

Fact 1 tells us that the AVERAGE number is equal to the LARGEST number. That can only happen when all 5 numbers are the SAME. Thus, the S.D. = 0
Fact 1 is SUFFICIENT

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

For the RANGE to be 0, all 5 numbers must be the SAME. Thus, the S.D. = 0
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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