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Website W receives orders for its products every day. What

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

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09 Oct 2013, 00:59
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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.

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.

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08 Oct 2013, 09:20
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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?
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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09 Oct 2013, 00:51
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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?
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.

hence Sufficient
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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.

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

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

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18 Oct 2015, 13:42
dubyap wrote:
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.
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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,
Khitindra
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Re: Website W receives orders for its products every day. What  [#permalink]

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13 May 2016, 22:33
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khitindra wrote:
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

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

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25 Jul 2017, 09:22
1
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.

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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

St 1

follows rule 1

suff

St 2

follows rule 2

suff

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

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30 Oct 2017, 04:14
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Hi Bunuel, any similar questions one could practice?
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Re: Website W receives orders for its products every day. What  [#permalink]

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30 Oct 2017, 04:20
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Re: Website W receives orders for its products every day. What  [#permalink]

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03 Jan 2018, 11:07
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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.

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

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12 Jun 2018, 02:06
What key words tell us that the question asks for average per day and not between days? I thought it asked for average of 5 days. If that's the case, statement 2 could be insufficient as:

Day 1: 3,3,3 orders
Day 2: 5,5,5 orders

Where range for each day could be 0 but SD between days could be anything. Thanks in advance.
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Re: Website W receives orders for its products every day. What  [#permalink]

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12 Jun 2018, 22:35
Andy24 wrote:
What key words tell us that the question asks for average per day and not between days? I thought it asked for average of 5 days. If that's the case, statement 2 could be insufficient as:

Day 1: 3,3,3 orders
Day 2: 5,5,5 orders

Where range for each day could be 0 but SD between days could be anything. Thanks in advance.

Hello

First statement clearly says, "Average (Arithmetic Mean) number of orders that Website W received each per day for the past 5 days...".

Second statement clearly says, "range of the number of orders that Website W received daily for the past 5 days..."

And the question does NOT ask for average per day, the question asks for Standard Deviation for the 5 days.
And your phrase 'average between days' is not clear.. can you please explain?
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Re: Website W receives orders for its products every day. What  [#permalink]

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03 Oct 2018, 12:46
Does statement 1 work if the mean = lowest? Same concept just the opposite extreme
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Re: Website W receives orders for its products every day. What  [#permalink]

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03 Oct 2018, 18:11
1
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.
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Re: Website W receives orders for its products every day. What   [#permalink] 03 Oct 2018, 18:11

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