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Understanding Statistics thread

Hello. I have heard Statistics (S1) is easy but am having trouble understanding Discrete random variables, the normal distribution and correlation and regression- the rest seems just like GCSE content (easy).
There seem to be lots of long equations which don't have an explanation for.
Would anybody know whether statistics is about applying the formulas or should you understand them? - Also, how would you go about understanding them?
Would anybody also know why we use the standard deviation when numbers further away from the mean are over- weighted compared to values close to the mean. It doesn't make sense why we do this and not just use the MAD.
Also, what's the difference between the SD and the variance?
I am thankful for any help.

Reply 1

TenOfThem

Original post by MathMeister

personally i think it is a mix

for e.g. the normal distribution is easy if you understand it - just a bit of graph transformations and an understanding of symmetry

whereas the sexy equations are horrible so i just "use them"

Reply 2

MathMeister

What are

Original post by TenOfThem

the sexy equations

Reply 3

TenOfThem

Original post by MathMeister

What are

Sxx
Syy
Sxy

Reply 4

davros

Original post by MathMeister

Would anybody also know why we use the standard deviation when numbers further away from the mean are over- weighted compared to values close to the mean. It doesn't make sense why we do this and not just use the MAD.Also, what's the difference between the SD and the variance?
I am thankful for any help.

This is partly historical and partly for technical reasons - if you're doing advanced things like differentiating statistical functions it's easier to deal with squares and square roots than it is to manipulate things inside modulus signs! The practical answer to your question is that you're going to see the standard deviation crop up in all sorts of places if you do any statistical work in the future, so you need to be comfortable with how it's worked out!

SD is the square root of the variance.

Reply 5

queensboy

Original post by TenOfThem

Sxx
Syy
Sxy

Your advise on this forum has truly been outstanding. From what i've seen over the years.

You really should be nominated to be a moderator.

Reply 6

Old_Simon

Always a bad idea to be using formulas or "equations" you do not know and understand.

Reply 7

MathMeister

Original post by queensboy

Your advise on this forum has truly been outstanding. From what i've seen over the years.
You really should be nominated to be a moderator.

True

Original post by davros

...SD is the square root of the variance.

Is it that the SD is the measure of how spread out values are from the mean and variance is how spread out values are from each other?

Original post by Old_Simon

Always a bad idea to be using formulas or "equations" you do not know and understand.

I like understanding every equation I may need to use. Usually, this also helps learn the topic very well.

(edited 9 years ago)

Reply 8

davros

Original post by MathMeister

True

Is it that the SD is the measure of how spread out values are from the mean and variance is how spread out values are from each other?

No, the SD is as you say and the variance is just the square of the SD (it doesn't have a natural interpretation because it's in squared units which aren't particularly helpful, e.g. if you're measuring masses in kg then the variance will be in kg^2 which isn't a useful unit!!)