Lesson: More Standard Deviation

Comment on More Standard Deviation

Hi Brent ,
These videos are great and very helpful. I was faced with same problem m+d one unit above/below the mean and i was able to tackle the question within a min. Thank you so much these videos are straight up to the point.

Thanks again !!!!
gmat-admin's picture

Hi Laxmi,
Thanks for taking the time to say that!

Perfect explanation and I save time

Hello Brent,

Can you please help me with the below question ?

What is the standard deviation of a set of numbers whose mean is 20?

(1) The absolute value of the difference of each number in the set from the mean is equal

(2) The sum of the squares of the differences from the mean is greater than 100

Since the absolute value of difference of each number from mean is equal, SD must be zero. I selected A as answer.

Thank you,
Srividhya
gmat-admin's picture

Good question.

Notice that the sets {-1, 1} and {-500, 500} both have a mean of 0, and the difference of each number in the set from the mean is equal. HOWEVER, the standard deviation in the 2nd set is much greater than the standard deviation in the 1st set

There are some nice solutions here: http://www.beatthegmat.com/what-is-the-standard-deviation-of-a-set-of-nu...

Cheers,
Brent

Pls help with the following question (will be helpful if you can highlight the concept that has been applied to the question):

A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?

(A) 16%
(B) 32%
(C) 48%
(D) 84%
(E) 92%
gmat-admin's picture

Brent,

Could you help me with the exercise #392 of OG17.

Thanks,
Pedro
gmat-admin's picture

You bet, Pedro.

Here's my solution: https://gmatclub.com/forum/beginning-in-january-of-last-year-carl-made-d...

Cheers,
Brent

Thanks Brent!

Cheers,
Pedro

Hi Brent, the following question is seeming to be tricky? I understand that there won't be any value besides the mean itself and as per my understanding of the question, it asks for the number of integer values within 3 units of SD of the mean. My answer - A) ZERO

A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values are within three standard deviations of the mean?

A. 0
B. 1
C. 3
D. 6
E. 7
gmat-admin's picture

Hi Jalal,

The correct answer is B (1).
Given the above information, the values within 3 standard deviations of the mean are all values from -1 3/8 to -5/8 inclusive.
So, the integer -1 is within this range.

Here's my full solution: https://gmatclub.com/forum/a-bell-curve-normal-distribution-has-a-mean-o...

Cheers,
Brent

https://gmatclub.com/forum/set-b-has-7-members-and-x-and-y-are-distinct-positive-integers-if-x-237195.html
sir i did this question by testing options 9,10 and 16 since x is mode only these option satisfy is their any other way other than testing values?
gmat-admin's picture

Question link: https://gmatclub.com/forum/set-b-has-7-members-and-x-and-y-are-distinct-...

Using the 2 facts (mean = 12 and mode = x), there are only 3 possible cases:
i) x = 9 and y = 15
ii) x = 10 and y = 13
iii) x = 16 and y = 1

To maximize the Standard Deviation, we must find the pair of values that are farthest from the mean (mean = 12)
x = 16 and y = 1 are the farthest from the mean.

So, x = 16 will maximize the Standard Deviation

Here's my full solution: https://gmatclub.com/forum/set-b-has-7-members-and-x-and-y-are-distinct-...

Cheers,
Brent

https://gmatclub.com/forum/if-s-is-a-set-of-four-numbers-x-y-z-and-w-is-the-range-of-the-numbe-249456.html
please explain .
gmat-admin's picture

https://gmatclub.com/forum/the-average-arithmetic-mean-of-10-distinct-odd-integers-in-a-set-is-244638.html
please explain.
gmat-admin's picture

Question link: https://gmatclub.com/forum/the-average-arithmetic-mean-of-10-distinct-od...

I'm a HUGE fan of Bunuel's questions on GMAT Club, but this questions requires WAYYYY too much brute force (fiddling with various 10-value sets) for it to be a true GMAT question.

I suggest that you skip this one.

Cheers,
Brent

https://gmatclub.com/forum/if-all-members-of-set-x-are-positive-integers-what-is-the-range-of-se-227980.html
please explain.
gmat-admin's picture

Hi Brent,

I have a question in general: When (in which scenarios) do we use variance over SD in real world applications and vice versa?

Warm Regards,
Pritish
gmat-admin's picture

Variance and Standard Deviation are very closely related.
In fact, √variance = standard deviation

Aside from the question in the Official Guide's diagnostic test, I don't think I've seen an OFFICIAL GMAT question that asks us to find the variance.

The main reason for this is that variance ends up with units of measurement that are DIFFERENT from the original data.

For example, let's say we're examining a set of temperatures in degrees Celsius {10, 20, 30}

The VARIANCE = the average of the sum of the squares of the differences between each value and the mean.

With the set {10, 20, 30}, the mean is 10.

So, the variance = [(10-20)² + (20-20)² + (30-20)²]/3

Let's examine one part: (30-20)²
30 - 20 = 10, tells us that 30 degrees is 10 degrees more than the mean of 20 degrees.
However, when we SQUARE (30-20)² to get 100, the units of measurement are now in degrees², which makes little sense.

However, when we find the standard deviation (by taking the square root of the variance), the unit of measurement is now in degrees (which makes sense)

Does that help?

Cheers,
Brent

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