Just wanted to give a summary of Standard Deviation and what

Question

Just wanted to give a summary of Standard Deviation and what it means. I know this was a little difficult for me to understand at first, so hopefully someone will find it useful. Just note, on the GMAT you will not need to solve any Standard Deviation questions, i.e. they give you a list of numbers and ask to find the S.D. You will need to understand what it means and what it stands for. Hopefully this will help explain, if not at least open a topic for discussion. :-D 

So let's start with the most basic question,  what is standard deviation? 

Let's start with a real life example:

Your CEO has just sent out an email to everyone in your company proud to announce that everyone will be getting an average salary of $100,000 next year. You should be excited, right? No, you are smarter than the average folk and decide to dig deeper into the numbers. :wink: Let's look at a couple of scenarios and see what you think (looking at a sample of 5 people):

 https://i17.photobucket.com/albums/b71/salr15/spelling-12.jpg 

As you can see all 3 scenarios have an average of $100,000.

Scenario 1 - Is the ideal scenario where everyone is making the same amount and everyone is happy.

Scenario 2 - This is probably what you are expecting when you see the email, a little fluctuation but nothing too bad,

Scenario 3 - This is what mostly likely is going on, where a few high salary people are bringing up the average.

So this is where Standard Deviation comes in to play, we want to find out how much the numbers    deviate    from the average.

I will solve one just to go through the formula, I would highly recommend you at least understand the formula but you won't have to memorize for the GMAT.

I will use Scenario 2 as an example:

Here are the steps to calculating S.D.:
1- Find the average of the list.
2- Subtract each term from the average.
3- square each of the differences.
4- add up all squared values.
5- Divide the sum by the number of terms.
6- Take the square root.

So lets look at Scenario 2 step by step:

 https://i17.photobucket.com/albums/b71/salr15/spelling-13.jpg 

So this means as the fluctuation increases, so does the Standard Deviation. So if you are the person making 30k, you are not going to be happy, the CEO promised an average of 100k!! This is why Standard Deviation is very useful and where averages can be a bit deceiving.

Now try solving this:

Which one of the following has the highest Standard Deviation:

1- 2, 5, 8, 10, 12
2- 6, 4, 8, 2, 10
3- 7, 10, 15, 20, 25

I would recommend going through the steps and finding the S.D. for each. This really helped me understand the formula and also the concept. Don't just try and memorize it.

So on test day when you get a DS that says (this is just a made up example):

What is the standard deviation of list x?

(1) x has a variance of 81. 

you will know this is sufficient because the square root of the variance is your standard deviation!

Hopefully we can get some good sample GMAT questions to follow. :-D

gowani · Answer

thanks for that 101....btw what is the answer to your question?

Which one of the following has the highest Standard Deviation:

1- 2, 5, 8, 10, 12
2- 6, 4, 8, 2, 10
3- 7, 10, 15, 20, 25 

?

salr15 · Answer

There are two ways to do this:

1- would be just to look at the list. You can tell that the 3rd the greatest variance. You have numbers from 7 to 25.

2- To solve using formula:

I get,

1- approx 3.5 standard deviation
2- approx 2.8 
3- approx 6.5

KillerSquirrel · Answer

Excellent work salr15. you get my two golden stars ! :rotate

here is a good question, not on SD but still very much related: Set X has 5 numbers, thier average is greater than their median. Set Y has 7 numbers, their average is greater than their median also. If the 2 sets have no common number and are combined to a new set, is the average of the new set greater than its median? (A) The average of Y is greater than the average of X (B) The median of Y is greater than the median of X :-D

ian7777 · Answer

We have a free Standard Deviation lesson on our website. I think it's really good and you all should check it out.

https://www.integratedlearning.net/gmat/sample.asp

Feel free to post comments, as well. We're always trying to improve :-D

baer · Answer

My head was spinning on this question: I'll go with E though. Rarely do combined sets yield information if there are no bounds for each set. Do you have a simple solution to the above?

r019h · Answer

seems like E but also seems like E might be wrong.
what's the solution, killersquirrel?

KillerSquirrel · Answer

The answer is indeed (E)

 :-D

Just wanted to give a summary of Standard Deviation and what

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