Data Sufficiency

How is the answer D and not B
I am missing something with option 1. Please explain how option 1 is sufficient.[/spoiler]

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

Q: SD = ?

St1: Max value = mean value (for a period of 5 days). This statement essentially states that all the data values are same, thus SD = 0.
SUFFICIENT

St2: Max - Min (for 5 days) = 0, thus when the data values are placed in ascending order all the values are again same. SD = 0
SUFFICIENT

Answer D

mevicks 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 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.
b) The range of the numbers of orders that Website W received daily for the past 5 days is equal to 0.

Q: SD = ?

St1: Max value = mean value (for a period of 5 days). This statement essentially states that all the data values are same, thus SD = 0.
SUFFICIENT

St2: Max - Min (for 5 days) = 0, thus when the data values are placed in ascending order all the values are again same. SD = 0
SUFFICIENT

Answer D

Hi Mate,

Is there any rule which says if the Mean=max value then all the numbers are same or just testing value will do the job in this case.

rakeshd347 wrote: Hi Mate,

Is there any rule which says if the Mean=max value then all the numbers are same or just testing value will do the job in this case.

There is no rule as such but the statement is easy to visualize if you break it down into simple steps:

1) receives orders for its products every day --> Ok. So atleast we have some number of orders everyday for a period of 5 days
2) mean value is usually below the maximum value, but wait here I see that mean is actually equal to the max and also the number of days are not just one! so all the values have to be that last value. (the orders have to be +ive integers so (x+x+x+x+x)/5 = x)

If you want to consider pure algebra:
Let the orders in increasing order be a, b, c, d, MAX
(note that a < b < c < d < MAX)

(Sum of all the orders) = 5 * MAX
Now the only way the sum of the 5 numbers could be equal to five times the MAX number is that they all are MAX.
ie a = b = c = d = MAX

A states that average per day for last 5 days = greatest in last 5 days. It means that same no. of products was received on all 5 days. So S.D = 0.

B states that range is 0. It means that max and min values are same, which implies that all values are same. So S.D. = 0.

So, the answer is D

Brent@GMATPrepNow wrote:Great explanation, Vivek!

A big takeaway here is that, 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.

Cheers,
Brent

Hi Brent,

I knew that same numbers will have 0 SD. However, i got confused with the fact that Mean=Largest number means that all numbers are same. Specially with time limit under test conditions. vivek explained it though as clear as possible.