Question: Standard Deviation Conclusions

Comment on Standard Deviation Conclusions

I thought because you had -2, -3, -4...that you couldn't have 0 or anything positive. It had to be a negative. When can we assume, if we can, that a list of numbers are ascending or descending? For example, if we had 1,2,3,4 can the next number be -23? If so, could you explain why?
greenlight-admin's picture

We cannot make any assumptions about the numbers in a set UNLESS there's some statement that explicitly states the values are in ascending or descending order.

Nice explanation and a trick one tricky one.

I had a slight confusion regarding the set of numbers. It is that for standard deviation is it not required for the set of numbers to be in ascending order? Standard deviation only calculates the deviation of numbers (in set) from mean and the difference of each number from adjacent number. Is this understanding correct?
greenlight-admin's picture

The part that reads "...and the difference of each number from ADJACENT number" is not correct.

To calculate standard deviation, we don't have to arrange the values in ascending order, so the concept of ADJACENT does not affect the standard deviation.

You might be confusing standard deviation with median, since medians are calculated by first arranging the values in ascending order.

Here's our video on standard deviation: https://www.greenlighttestprep.com/module/gre-statistics/video/806

Cheers,
Brent

hey brent im not being able to comprehend how to choose the numbers here?
greenlight-admin's picture

Notice that both sets share 3 numbers: -2, -3 and -4
The mean of these 3 numbers is -3
We know that the standard deviation is greater when values are further away from the mean.

Since the standard deviation of set Q is greater than the standard deviation of set R, we know that q must be further away from the mean (-3) that r is away from the mean.

The key idea is that, there are two ways that q can be further away from the mean that r is:
1) q could be a very big negative value like -10,000 and r could be -3
2) q could be a very big positive value like 10,000 and r could be -3

In the first example, Quantity B is greater.
In the second example, Quantity R is greater.

Does that help?

Cheers,
Brent

Have a question about this video?

Post your question in the Comment section below, and Brent (the course creator) will answer it as fast as humanly possible.

Change Playback Speed

You have the option of watching the videos at various speeds (25% faster, 50% faster, etc). To change the playback speed, click the settings icon on the right side of the video status bar.

Let me Know

Have a suggestion to make the course even better? Email me today!

Free “Question of the Day” emails!