Website W receives orders for its products every day. What is the Stan

Question

Website W receives orders for its products every day. What is the Standard Deviation of the number of orders that Website W received daily for the past 5 days?

(1) The Average (Arithmetic Mean) number of orders that Website W received each per day for the past 5 days is equal to the greatest of the number of orders that Website W received daily for the past 5 days.

(2) The range of the number of orders that Website W received daily for the past 5 days is Zero.

Bunuel · Accepted Answer

Website W receives orders for its products every day. What is the Standard Deviation of the number of orders that Website W received daily for the past 5 days?

(1) The Average (Arithmetic Mean) number of orders that Website W received each per day for the past 5 days is equal to the greatest of the number of orders that Website W received daily for the past 5 days.

Since mean=greatest, then the number of orders each day was the same. This implies that the standard deviation is 0 (the standard deviation of a set is zero if and only the set consists of identical numbers). Sufficient.

(2) The range of the number of orders that Website W received daily for the past 5 days is Zero.

Basically the same here: since the range is 0 (greatest-smallest=0 --> greatest=smallest), then the number of orders each day was the same. Sufficient.

Answer: D.

Qoofi · Answer

Hi,

Standard Deviation = Sum of the square of the variations from mean / total number of entities.

Statement 1 : The average of number of orders = Greatest order of the day. 
Hence the variation = 0, so the SD = 0
Sufficient

Statement 2 : Range = Max value - min value

Here the range = 0

The number of orders = 0 ( Number of orders can't be negative)

So SD = 0
Sufficient

Both the statements are sufficient

Option D

Hope it is clear

Cheers
Qoofi

shameekv · Answer

For standard deviation you just need to know if the numbers in the sequence are in some particular order. For eg in case of consecutive numbers the deviation can be calculated. and if all the numbers in a particular sequence are same then the deviation will be 0.

Statement 1:- 
If the average of the numbers is equal to the greatest of all the numbers then all the numbers have to be that greatest number. Hence there is no deviation.

eg. 3,4,5 the greatest is 5 but average is 4. So it all the numbers have to be 5 for the average to be 5.

But if it were stated that the median is equal to the highest then it would have been insufficient since median can be the greatest number of those 5 days and the first 2 can be different.

hence Sufficient.

Statement 2:- 
If the range is 0, then the highest number of delivery - lowest number of delivery is 0.

So if the highest number in the sequence is equal to the lowest number in the sequence, all the numbers in that sequence has to be same.

hence Sufficient

khitindra · Answer

Hi Bunuel,

Thanks for your crystal clear explanation. However, i have a question. If the first option is written as :'The Average (Arithmetic Mean) number of orders that Website W received each per day for the past 5 days is equal to the least of the number of orders that Website W received daily for the past 5 days', what would be the answer. I believe it would be insufficient to answer using the first option. Please comment.

Thanks,
Khitindra

chetan2u · Answer

Hi  khitindra ,
If the sentence was- 
:'The Average (Arithmetic Mean) number of orders that Website W received each per day for the past 5 days is equal to the least of the number of orders that Website W received daily for the past 5 days

since average = least, this means all the orders are same ....
average can be equal to least or greatest ONLY when the orders are same...

say least and average are 10, so if any orders above this would change the average so all have to be SAME

BillyZ · Answer

Each statement says the same thing.  Range = 0 .

If the  mean = the max , then all the numbers are the same.

Try some sets of numbers to see, that will help on test day.

Say the mean is 5 and the max is 5

OK, then if I have any other number in the set. Say 4, {4, 5}, mean isn't 5 any more, too small

So all the numbers = 5

Answer :  D

sergioas22 · Answer

Another approach to solve this.

(1) Let's say: a<b<c<d<e
Average is equal to the greatest: (a+b+c+d+e)/5=e --> a+b+c+d+e=5e --> a+b+c+d = 4e
All elements are equal. Standard deviation is 0. Sufficient.

(2) If the range is 0 it means that all elements are equal, like in (1). So, sufficient too.

Answer: D.

nawaf52 · Answer

First, you need to understand the meaning of standard deviation. Standard deviation measures how far a certain point is from the mean. For example, let's consider the following data :
(1, 2, 3, 4, 5). The the mean of these data equal (1+2+3+4+5)/5 =15/5 = 3. Now, you can see that the largest point 5 and 1 are two points from the mean. 2 and 4 are 1 point from the mean. 3 is zero point from the mean. The range of our example is equal to the large value minus the smallest value (5-1=4)

Now, let's go back to the main question. 
1 telling you that the mean is equal to the greatest number in the set ( for example if the mean is 5 then the greatest and also the smallest numbers are 5 too . This means that all of the five days have the same number of orders thus each day is 0 point from the mean. This is sufficient.

2 is talking about the range. It's telling you that the largest number is equal the smallest number. This means that all of the numbers in the five years are equal, thus each and each day is zero point from the mean. This is sufficient too.

nikhilc11 · Answer

Hi Bunuel, any similar questions one could practice?

Bunuel · Answer

*  Standard Deviation Questions  from our  Special Questions Directory .

20. Descriptive Statistics 
     Theory   
 Statistics Made Easy - All in One Topic! 
 GMAT Statistics 101 
 Math: Standard Deviation 
 How to Quickly Solve Standard Deviation Questions on the GMAT 
     Questions   
 Standard Deviation Problems 
 DS Questions 
 PS Questions

For more check:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Hope it helps.

ScottTargetTestPrep · Answer

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.

Answer: D

bpdulog · Answer

Does statement 1 work if the mean = lowest? Same concept just the opposite extreme

LauraOrion · Answer

Hey  bpdulog  - Yes, it would still work! What you get out of the information that mean = highest number in the original statement is that all the numbers have to be the same. Think about it this way, if they were different (say the numbers were 11, 12, and 13), you could never get the mean to be equal to the highest number because it's going to be somewhere between the highest number and the lowest number. By the same logic, for the mean to be equal to the lowest number, you'd need all numbers to be equal since the mean will be somewhere between the lowest number and the highest number.

Diwabag · Answer

Hi  Bunuel  , and  ScottTargetTestPrep  ,  chetan2u  ,  GMATNinja

I need help in understanding statement 1. What threw me off was the word GREATEST. How can you say that the average is equal to the GREATEST number of orders if all the orders received for the past 5 days are equal?

When you say GREATEST, doesn't it mean that other values are supposed to be LESSER? How can you say it's GREATEST if they're all equal?

What am I missing here?

Thanks.

ScottTargetTestPrep · Answer

It might be useful to interpret “greatest” as “no other value is greater” rather than “all other values are lesser.” So, the values can all be equal. If the average is equal to the greatest number in the set, that is another way to say that all values MUST BE THE SAME. In fact there is no other possible way for the average to equal the greatest value in the set, unless all values are the same. (Note: The same thing is true if the average is equal to the smallest number in the set.)

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