Lesson: More Standard Deviation

Comment on More Standard Deviation

Hi Brent, could you possibly help me with this question?
https://greprepclub.com/forum/the-mean-of-a-set-of-data-with-a-standard-deviation-of-12761.html

The mean of a set of data with a standard deviation of 0.32 is 4.45.

Which of the following numbers fall between 2 and 3 standard deviations away from the mean?

Indicate all possible values.

Im confused here. It says for us to find the values of numbers that are AWAY from the mean, therefore we'd pick our numbers to the left of the mean on the number line.

Heres my worK:

for 2 SD away: 4.45-.32-.32= 3.81
for 3 SD away: 4.45-.32-.32-.32= 3.49

therefore, this makes the choices between 3.49 and 3.81.

Since It says AWAY, why is answer D correct?
I understand how to calculate the SD above the mean. If the question stated Above, then answer D would be correct, no?

Thanks so much!
greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-mean-of-a-set-of-data-with-a-standard-...

For the purposes of standard deviation questions, AWAY = ABOVE and BELOW
So, for example, 2 standard deviations AWAY from the mean = 2 standard deviations ABOVE the mean, and 2 standard deviations BELOW the mean.

If the question said ABOVE the mean, then the correct answer would be D.

Likewise, on the NUMBER LINE, if I say that point Q is 2 units AWAY from 5, we can conclude that Q = 3 or Q = 7

Does that help?

Cheers,
Brent

Yes!!!! Thank you so much!! So the only term to truly watch out for is above, since it distinctly means only the numbers to the right.

Hi Brent,

If we would have those numbers in the set included, 7.6 and 16.4, should we count them too? Meaning, when we say within one standard deviation from the mean, should we include the edges as well? Thanks
greenlight-admin's picture

Good question!
If the question says "within one standard deviation" the must include values that are exactly one standard deviation away from the mean.

https://greprepclub.com/forum/in-a-population-of-chickens-the-average-arithmetic-mean-15623.html
At the question like above is there any special phrase that shows us as a sign, we should consider x Units above and or Unit below standard deviation or when asking "within x units of the standard deviation of the mean" it means we should consider both scenarios (above & below).

Your reply is highly appreciated
greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-a-population-of-chickens-the-average-ar...

It's hard to create a rule that encompasses all possible scenarios.
Instead, let's examine some possible wordings and what that each wording tells us to do.

Let's say a distribution of ages has a mean of 72 and a standard deviation of 10.
Now let's examine some possible questions:

What ages are more than one standard deviation above the mean?
Here, we want all ages that are greater than 82.

What ages are more than two standard deviations below the mean?
Here we want all ages that are less than 52.

What ages are within three standard deviations of the mean?
Here we want all ages that are between 42 and 102

What ages are more than three standard deviations away from the mean?
Here we want all ages that are less than 42 OR greater than 102.

Does that help?

https://gmatclub.com/forum/the-monthly-sales-in-thousands-of-at-a-certain-restaurant-190840.html

Could you please explain why the answer is A i thought it would be C?
greenlight-admin's picture

Question link: https://gmatclub.com/forum/the-monthly-sales-in-thousands-of-at-a-certai...
(Aside: Even though this question is taken from a GMAT forum, it could easily apply to questions on the GRE)

If this year's standard deviation is greater than last year's, we know that this year's data is more spread apart than last year's data.
Applying the informal definition of standard deviation, we know that the average distance from the mean of this year's data is greater than the average distance from the mean of last year's data.

We have the following:
Last Year: 9, 9.5, 10, 10, 11, 11, 11, 11, 11, 12.5, 13, 13
This Year: 9, X, 10, 10, 11, 11, 11, 11, 11, Y, 13, 13

In last year's data, it appears that the mean is approximately 11.
So, we can increase this year's standard deviation the most by adding two values (X and Y) that are as far away from 11 as possible.

A) 9 and 12.5
C) 10 and 12.5

We can see that the pair of values 9 and 12.5 are further away from 11 than the pair of values 10 and 12.5 are.

So, adding 9 and 12.5 to the data will increase the standard deviation more then adding 10 and 12.5 to the data.

Does that help?

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