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Website W receives orders for its products every day. What [#permalink]

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08 Oct 2013, 09:01

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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.

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? a) 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. b) The range of the number of orders that Website W received daily for the past 5 days is Zero.

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
_________________

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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? a) 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. b) The range of the number of orders that Website W received daily for the past 5 days is Zero.

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.

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.

Re: Website W receives orders for its products every day. What [#permalink]

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08 Dec 2014, 09:50

Bunuel wrote:

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.

Hi Bunuel,

Can you please explain statement 1 with some kind of mathematical equation? I know it seems kind of silly of me but for the life of me i cant seem to wrap my head around it

Re: Website W receives orders for its products every day. What [#permalink]

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13 Oct 2015, 22:12

Out of curiosity, how do you guys know the difficulty range of these questions (i.e. 600-700) or are these just guesses on the part of the thread originator?

Out of curiosity, how do you guys know the difficulty range of these questions (i.e. 600-700) or are these just guesses on the part of the thread originator?

The difficulty level is calculated automatically based on users answers.
_________________

Re: Website W receives orders for its products every day. What [#permalink]

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13 May 2016, 22:28

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 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

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
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Re: Website W receives orders for its products every day. What [#permalink]

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18 May 2017, 18:03

imhimanshu wrote:

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.

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 _________________

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Website W receives orders for its products every day. What [#permalink]

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25 Jul 2017, 09:22

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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.

Re: Website W receives orders for its products every day. What [#permalink]

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10 Sep 2017, 22:02

imhimanshu wrote:

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.

Housekeeping tips

-If the min or max equals the mean(average) then the standard deviation is 0

-If the range of the set is zero this means the standard deviation is 0

Please help why the below DS problem results in D as the correct answe [#permalink]

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13 Oct 2017, 20:54

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 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.

Re: Please help why the below DS problem results in D as the correct answe [#permalink]

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13 Oct 2017, 21:31

sophieyu0717 wrote:

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 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.

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.

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 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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